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Go to
TeachMeFinance.com – read topics:
a. The Time Value of Money, Time Value of Money – Future Value and Present Value – How to calculate it (
http://teachmefinance.com/timevalueofmoney.html
)
b. Annuities, Teachmefinance.com/annuities (
http://teachmefinance.com/annuities.html
)
c. Perpetuities, teachmefinance.com/ perpetuity (
http://teachmefinance.com/perpetuities.html
)
d. Future value of an uneven cashflow (
http://teachmefinance.com/futurevalueofanunevencashflow.html
)
Discussion 1 – Time Value of Money
Read three articles in the links below about affinity credit cards and schools. After reading this,
· Do you think universities should enter into agreements to offer affinity credit cards to students? Why or why not? Discuss the ethics of these offerings.
Credit Cards and Campuses:
https://www.insidehighered.com/news/2010/02/19/credit-cards-and-campuses
The Dirty Secret of Campus Credit Cards
:
The Dirty Secret of Campus Credit Cards
Read the article: Warren Buffet on Credit Card Debt
https://www.cnbc.com/2020/05/13/warren-buffett-cautions-against-carrying-a-credit-card-balance.html
Also, find websites that calculate or explain NPV or any other Financial Concepts we have learned about. What have you found?
Link: https://leocontent.umgc.edu/content/umuc/tus/finc/finc331/2228/modules/finc330/m2-
module-2/s3-commentary.html#I
UMGC Module 2: Financial Securities
Topics
The Time Value of Money
The Time Value of Money
Arguably, the time value of money concept is the most fundamental concept in the study of
finance. It basically states that a dollar received today is worth more than a dollar received
tomorrow. The underlying reason for this statement is that it is assumed that the dollar received
today can be invested and earn some interest before the dollar received tomorrow, whereas the
dollar to be received tomorrow obviously cannot earn interest today. Logically, this means a
dollar to be received in the future must somehow be discounted, or adjusted in value, to be
financially comparable to a dollar received in the present.
Extrapolating on this principal, logically, if we are to compare the expected return of alternative
projects, strategies, and investments over varying periods of time, we must first convert all the
dollars received at the various times in the future back to their present-day value. This process is
called present value.
Alternatively, we could achieve the same desired comparable results by moving all the dollars
received at various times out to some common future date. This process is called future value.
Only when the alternative investment cash flows are compared in dollar values of the same date
is the financial evaluation of alternative returns meaningful.
The Concept of Compound Interest and Future Value
Although most financial analysis is conducted from the perspective of present value, we will
begin our discussion of the time value of money concept with future value because it is easier to
understand. We start by considering the term compound interest. It occurs when the interest paid
on an investment during the first period is added to the principal, and during the second period
interest is earned on both the principal and the prior period interest.
There are three methods of calculating compound interest—longhand, equation, and financial
tables. Using the following scenario, we’ll go through each method. Consider $100 invested for
three years earning compounded interest at an annual rate of 6% per year.
https://leocontent.umgc.edu/content/umuc/tus/finc/finc331/2228/modules/finc330/m2-module-2/s3-commentary.html#I
https://leocontent.umgc.edu/content/umuc/tus/finc/finc331/2228/modules/finc330/m2-module-2/s3-commentary.html#I
https://leocontent.umgc.edu/content/umuc/tus/finc/finc331/2228/modules/finc330/m2-module-2/s3-commentary.html#I
1. Longhand—This method can be tedious, especially if you’re calculating the compound
interest over 10 or 20 years.
Beginning of
year 1
= $100 = $100.00
End of year 1
(FV1)
= $100 + $100(.06) = $106.00
End of year 2
(FV2)
=
[$100 + $100(.06)] + [$100 + $100 (.06)] (.06)
or $106.00 + $106 (.06)
=
$112.36
$112.36
End of year 3
(FV3)
= $112.36 + $112.36 (.06) = $119.10
The above mathematical progression can be generalized into the following formula for
calculating the compound or future value (FV) on any present value (PV) amount given
these two variables, the discount rate per period (i) and the number of periods (n).
2. Compound interest or future value equation—This method is much cleaner and
quicker than the longhand method.
FVn = PV(1 + i)n
where:
FVn = future value at the end of n periods
PV = present value, or the original amount, deposited at the beginning of
period
n = number of periods of compounding = 3
i = interest rate per period = 6%
Please note that in the generalized formula, we specifically used the term periods and not
years because mathematically the general formula derived applies for any given period of
time (years, quarters, weeks, or days). Financially, we typically see compounding
annually, semiannually, or quarterly.
3. Financial tables—You can find these future value (compound sum of $1) tables at the
back of your textbook. They may make compounding interest easier than do the other
two methods.
Also note that the (1 + i)n factor in the tables will work for any amount PV. Simply
multiply the amount by the factor (l + i)n. Given this relationship, financial tables can be
constructed for all reasonable combinations of interest rate per period and number of
periods. We recommend that you look at financial tables for the compound sum of $1 for
various interest rates and periods.
If you check the table for the interest rate of 6% for years 1, 2, and 3, you will find the
following factors:
i = 6%, n = 1 —– = 1.060
i = 6%, n = 2 —– = 1.124
i = 6%, n = 3 —– = 1.191
Multiply these factors by the PV of $100, shown in our above-illustrated example, and you get
the following amounts, which, adjusted for rounding, match the solutions in our compounding
example:
i = 6%, n = 1 —– = 1.060 ($100) = $106.00
i = 6%, n = 2 —– = 1.124 ($100) = $112.40 *difference caused by rounding
i = 6%, n = 3 —– = 1.191 ($100) = $119.10
This example illustrates how the compounding formula developed for future value calculations is
used to construct the standard financial compounding tables found in all finance textbooks. The
compounding formula rewritten to allow easy use of the data in the compound financial tables is:
where FVIFi, n represents the appropriate financial table compounding factor for interest rate i
and periods n.
It is important for you to be able to solve future-value financial problems by financial calculator,
mathematical calculation, or financial tables. We recommend making the investment, in cash and
time, in a financial calculator. It is a significant time saver in this course and may have uses in
your future professional and personal endeavors.
Also, you should note that most time-value-of-money problems, including compound-interest
problems, can be solved by spreadsheet formulas, such as those included in Microsoft Excel.
Because computers are not allowed in the proctored final examinations, however, the spreadsheet
method of solution is not emphasized in this course.
Moving from the Future-Value to the Present-Value Concept
As stated earlier, in practice financial management generally has a greater use for present value
than future value, and typically we discount all future cash flows back to the present for proper
comparative financial analysis and decision making. Determining the present value—that is, the
value in today’s dollars of a sum (or stream) of cash flows to be received in the future—is
nothing other than the inverse of compounding. The difference in these techniques comes about
merely from the investor’s perspective in time.
Mathematically, the present value (PV) formula can be derived by algebraically rearranging the
compounding formula developed above to solve for the PV:
FVn = PV(1 + i)n
Rearrange the future value formula to algebraically solve for PV, and you obtain:
PV = FVn/(1 + i)n
where again:
FVn = future value at the end of n periods
PV = present value, or original amount, at the beginning of period 1
n = number of periods of discounting
i = interest rate per period
Again, similar to the compound-value formula, PV financial tables can be constructed using this
formula. They can be constructed in two ways, either by using the present value (PV) formula or
by dividing the FVIF table values into 1, because, by definition, the PV is the reciprocal of the
future value (FV). Once these tables are constructed, they can be used to solve PV discounting
problems with the following formula:
PV = FVn (PVIF i,n)
where PVIFi,n represents the appropriate financial table discounting factor for interest rate i, and
periods n. These PV factors are shown in the present value of $1 table in your textbook.
Future-Value/Present-Value Relationship to Variables
It is important that you understand that compounding (future value) and discounting (present
value) are reciprocals of each other. If you know either factor, you can calculate the other by
taking the reciprocal. To illustrate the inverse relationship between compounding and
discounting, the following presentation will show the graphical effect of compounding and
discounting $100.00 for five years at interest rates of 0%, 5%, and 10%.
Future-Value/Present-Value Relationship to Variables
The following presentation will show the graphical effects of first compounding and then
discounting $100.00 over a five-year period at interest rates of 0 percent, 5 percent, and 10
percent.
You should now set up and solve several simple financial problems for both present value and
future value to understand clearly what happens to each of these values as the interest rate (i) and
number of periods (n) change. One way to do so is to use the above graphical problem and solve
two consecutive years (3, 4) for all three rates (0%, 5%, and 10%). Be sure to change only one
variable at a time. Make a table of the results, and you should see clearly the inverse relationship
of present value to future value, as shown in the graphical presentation above.
https://leocontent.umgc.edu/content/umuc/tus/finc/finc331/2228/modules/finc330/m2-module-2/popups/graphic1-mod2.html
Annuities (Future Value and Present Value)
With the present/future value concepts understood, we can now discuss another common
financial application that is used in bonds, interest payments, pensions, and so forth—the
annuity. An annuity is the special case cash flow where a series of equal dollar payments is made
for a specified number of periods. Typically, financial management is interested in determining
either the future value or present value of an annuity.
The Future Value of an Annuity
It is important to remember that the period payment amount in an annuity must be a constant for
all periods. The development of the general annuity formula for the future-value case (a
compound annuity) is based on the constant-payment amount (PMT) and the previously
developed formula for calculating future value (1 + i)t. This is illustrated below for the future
value of a three-year annuity of $500 for three years at 6%:
FV3 = (PMT)(1 + i)3 + (PMT)(1 + i)2 + (PMT)(1 + i)1 + (PMT)
Obviously, this formula can be reduced to a general formula by factoring out the period payment,
PMT, and summing the discounted year payments from t = 1 to n – 1 periods, as shown below:
The future value formula for an annuity.
where:
FVn = future value of the annuity
(PMT) = constant payment deposited or received each period
i = interest rate per period
n = number of periods
The future value of an annuity can also be expressed in the alternative financial table format:
FVn = PMT (FVIFAi, n)
where:
The Future value of an Annuity Factor
The Present Value of an Annuity
The development of a general formula for the present value of an annuity is the reciprocal of the
future value of an annuity and follows the same logical progression to arrive at:
where:
PV = present value of the future annuity
(PMT) = constant payment deposited or received each period
i = interest rate per period
n = number of periods
Or expressed in financial table format:
PV = PMT (FVIFA i, n) The present value of an annuity factor.
Present Value of an Uneven or Complex Cash Flow
In the real world, the majority of cash flows that must be financially analyzed are typically not
single cash flows or equal-payment annuities, but rather cash streams with varying amounts per
period. This type of cash flow is called complex cash flow and requires a special approach to
determine its present value. The present value of a complex cash flow stream can always be
found by discounting the cash flows for each individual year by multiplying the present value
interest factor for that year (PVIFi, n) times the cash flow amount. The advantages of this
approach are that it is simple, accurate, always works, and does not require memorization of any
complex formulas.
For example, let’s compute the PV of the following complex cash stream, assuming a discount
rate of 6%.
Year $ Amount Factor (6%)* Discounted Amount
0.00 1.000 0.00
1 500.00 0.943 471.70
2 200.00 0.890 178.00
3 (400.00) 0.840 (335.84)
4 500.00 0.792 396.04
5 300.00 0.747 224.17
Total 1,100.00
Net present value $993.60
*From financial tables
Note that this answer developed using financial table values differs slightly from the
mathematical formula approach:
Manual method (above) ———- $933.50
Financial calculator ————— $934.07
This is not an unusual case, and slight differences between methods occur frequently because of
the number of significant digits used in the various methods of calculation. Both answers are
acceptable in this course.
Although this is a laborious method if calculated by use of either the financial tables or a regular
calculator, it becomes a relatively simple and quick method if one uses the cash-flow feature of
the financial calculator. We recommend taking the time to learn this method on your financial
calculator because you will encounter complex cash flows several times in this course.
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The Time Value of Money
Introduction to the Time Value of Money
Future Value, Single Amount
Present Value, Single Amount
Annuities
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Valuing Multiple Cash Flows
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The Time Value of Money
(continued)
Additional Detail on Present and Future Values
Yield
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Defining the Time Value of Money
Importance of the Time Value of Money
Introduction to the Time Value of Money
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Being given $100 today is better than being given $100 in the future because you don’t have to wait for your money.
Money today has a value (present value, or PV) and money in the future has a value (future value, or FV).
The amount that the value of the money changes after one year is called the interest rate (i). For example, if money today is worth 10% more in one year, the interest rate is 10%.
Defining the Time Value of Money
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Simple Interest Formula
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The Time Value of Money > Introduction to the Time Value of Money
Money today is worth more than the same quantity of money in the future. You can invest a dollar today and receive a return on your investment.
Loans, investments, and any other deal must be compared at a single point in time to determine if it’s a good deal or not.
The process of determining how much a future cash flow is worth today is called discounting. It is done for most major business transactions during investing decisions in capital budgeting.
Importance of the Time Value of Money
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Compound Interest
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Multi-Period Investment
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Single-period investments use a specified way of calculating future and present value.
Single-period investments take place over one period (usually one year).
In a single-period investment, you only need to know two of the three variables PV, FV, and i. The number of periods is implied as one since it is a single-period.
Single-Period Investment
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The Time Value of Money > Future Value, Single Amount
Investments that accrue simple interest have interest paid based on the amount of the principal, not the balance in the account.
Investments that accrue compound interest have interest paid on the balance of the account. This means that interest is paid on interest earned in previous periods.
Simple interest increases the balance linearly, while compound interest increases it exponentially.
Multi-Period Investment
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Simple Interest Formula
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The Time Value of Money > Future Value, Single Amount
The future value is the value of a given amount of money at a certain point in the future if it earns a rate of interest.
The future value of a present value is calculated by plugging the present value, interest rate, and number of periods into one of two equations.
Unless otherwise noted, it is safe to assume that interest compounds and is not simple interest.
Calculating Future Value
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Compound Interest
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The Time Value of Money > Future Value, Single Amount
The “present” can be moved based on whatever makes the problem easiest. Just remember that moving the date of the present also changes the number of periods until the future for the FV.
To find FV, you must first identify PV, the interest rate, and the number of periods from the present to the future.
The interest rate and the number of periods must have consistent units. If one period is one year, the interest rate must be X% per year, and vis versa.
Approaches to Calculating Future Value
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Compound Interest
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The Time Value of Money > Future Value, Single Amount
Single-Period Investment
Multi-Period Investment
The Discount Rate
Number of Periods
Calculating Present Value
Present Value, Single Amount
The Time Value of Money > Present Value, Single Amount
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A single period investment has the number of periods (n or t) equal to one.
For both simple and compound interest, the PV is FV divided by 1+i.
The time value of money framework says that money in the future is not worth as much as money in the present.
Single-Period Investment
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FV of a single payment
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The Time Value of Money > Present Value, Single Amount
Finding the PV for a multi-period investment is the same as for a single-period investment: plug FV, the interest rate, and the number of periods into the correct formula.
PV varies jointly with FV, and inversely with i and n.
When n>1, simple and compound interest cease to provide the same answer (unless the interest rate is 0).
Multi-Period Investment
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The Time Value of Money > Present Value, Single Amount
The discount rate represents some cost (or group of costs) to the investor or creditor.
Some costs to the investor or creditor are opportunity cost, liquidity cost, risk, and inflation.
The discount rate is used by both the creditor and debtor to find the present value of an amount of money.
The Discount Rate
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The Time Value of Money > Present Value, Single Amount
A period is just a general term for a length of time. It can be anything- one month, one year, one decade- but it must be clearly defined and fixed.
For both simple and compound interest, the number of periods varies jointly with FV and inversely with PV.
The number of periods is also part of the units of the discount rate: if one period is one year, the discount rate must be defined as X% per year. If one period is one month, the discount rate must be X% per month.
Number of Periods
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FV of a single payment
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The Time Value of Money > Present Value, Single Amount
The first step is to identify if the interest is simple or compound. Most of the time, it is compound.
The interest rate and number of periods must have consistent units.
The PV is what a future sum is worth today given a specific interest rate (often called a “discount rate”).
Calculating Present Value
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The Time Value of Money > Present Value, Single Amount
Annuities
Future Value of Annuity
Present Value of Annuity
Calculating Annuities
Annuities
The Time Value of Money > Annuities
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Annuities have payments of a fixed size paid at regular intervals.
There are three types of annuities: annuities-due, ordinary annuities, and perpetuities.
Annuities help both the creditor and debtor have predictable cash flows, and it spreads payments of the investment out over time.
Annuities
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The Time Value of Money > Annuities
To find the FV, you need to know the payment amount, the interest rate of the account the payments are deposited in, the number of periods per year, and the time frame in years.
The first and last payments of an annuity due both occur one period before they would in an ordinary annuity, so they have different values in the future.
There are different formulas for annuities due and ordinary annuities because of when the first and last payments occur.
Future Value of Annuity
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The Time Value of Money > Annuities
The PV for both annuities-due and ordinary annuities can be calculated using the size of the payments, the interest rate, and number of periods.
The PV of a perpetuity can be found by dividing the size of the payments by the interest rate.
Payment size is represented as p, pmt, or A; interest rate by i or r; and number of periods by n or t.
Present Value of Annuity
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The Time Value of Money > Annuities
There are five total variables that go into annuity calculations: PV, FV, interest rate (i or r), payment amount (A, m, pmt, or p), and the number of periods (n).
The calculations for ordinary annuities and annuities-due differ due to the different times when the first and last payments occur.
Perpetuities don’t have a FV formula because they continue forever. To find the FV at a point, treat it as an ordinary annuity or annuity-due up to that point.
Calculating Annuities
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PV of a Perpetuity
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The Time Value of Money > Annuities
Future Value, Multiple Flows
Present Value, Multiple Flows
Valuing Multiple Cash Flows
The Time Value of Money > Valuing Multiple Cash Flows
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The FV of multiple cash flows is the sum of the FV of each cash flow.
To sum the FV of each cash flow, each must be calculated to the same point in the future.
If the multiple cash flows are a fixed size, occur at regular intervals, and earn a constant interest rate, it is an annuity. There are formulas for calculating the FV of an annuity.
Future Value, Multiple Flows
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FV of a single payment
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The Time Value of Money > Valuing Multiple Cash Flows
To find the PV of multiple cash flows, each cash flow much be discounted to a specific point in time and then added to the others.
To discount annuities to a time prior to their start date, they must be discounted to the start date, and then discounted to the present as a single cash flow.
Multiple cash flow investments that are not annuities unfortunately cannot be discounted by any other method but by discounting each cash flow and summing them together.
Present Value, Multiple Flows
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Sum FV
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The Time Value of Money > Valuing Multiple Cash Flows
The Relationship Between Present and Future Value
Calculating Perpetuities
Calculating Values for Different Durations of Compounding Periods
Comparing Interest Rates
Calculating Values for Fractional Time Periods
Loans and Loan Amortization
Additional Detail on Present and Future Values
The Time Value of Money > Additional Detail on Present and Future Values
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The future value (FV) measures the nominal future sum of money that a given sum of money is “worth” at a specified time in the future assuming a certain interest rate, or more generally, rate of return. The FV is calculated by multiplying the present value by the accumulation function.
PV and FV vary jointly: when one increases, the other increases, assuming that the interest rate and number of periods remain constant.
As the interest rate (discount rate) and number of periods increase, FV increases or PV decreases.
The Relationship Between Present and Future Value
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FV of a single payment
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The Time Value of Money > Additional Detail on Present and Future Values
Perpetuities are a special type of annuity; a perpetuity is an annuity that has no end, or a stream of cash payments that continues forever.
To find the future value of a perpetuity requires having a future date, which effectively converts the perpetuity to an ordinary annuity until that point.
Perpetuities with growing payments are called Growing Perpetuities; the growth rate is subtracted from the interest rate in the present value equation.
Calculating Perpetuities
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The Time Value of Money > Additional Detail on Present and Future Values
The units of the period (e.g. one year) must be the same as the units in the interest rate (e.g. 7% per year).
When interest compounds more than once a year, the effective interest rate (EAR) is different from the nominal interest rate.
The equation in skips the step of solving for EAR, and is directly usable to find the present or future value of a sum.
Calculating Values for Different Durations of Compounding Periods
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EAR with Continuous Compounding
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The Time Value of Money > Additional Detail on Present and Future Values
A nominal interest rate that compounds has a different effective rate (EAR), because interest is accrued on interest.
The Fisher Equation approximates the amount of interest accrued after accounting for inflation.
A company will theoretically only invest if the expected return is higher than their cost of capital, even if the return has a high nominal value.
Comparing Interest Rates
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Fisher Equation
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The Time Value of Money > Additional Detail on Present and Future Values
The balance of an account only changes when interest is paid. To find the balance, round the fractional time period down to the period when interest was last accrued.
To find the PV or FV, ignore when interest was last paid an use the fractional time period as the time period in the equation.
The discount rate is really the cost of not having the money over time, so for PV/FV calculations, it doesn’t matter if the interest hasn’t been added to the account yet.
Calculating Values for Fractional Time Periods
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Compounding Interest
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The Time Value of Money > Additional Detail on Present and Future Values
Each amortization payment should be equal in size and pays off a portion of the principal as well as a portion of the interest.
The percentage of interest versus principal in each payment is determined in an amortization schedule.
If the repayment model for a loan is “fully amortized,” then the very last payment pays off all remaining principal and interest on the loan.
Loans and Loan Amortization
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Amortization Schedule
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The Time Value of Money > Additional Detail on Present and Future Values
Calculating the Yield of a Single-Period Investment
Calculating the Yield of an Annuity
Yield
The Time Value of Money > Yield
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There are a number of ways to calculate yield, but the most common ones are to calculate the percent change from the initial investment, APR, and APY (or EAR).
APR (annual percentage rate) is a commonly used calculation that figures out the nominal amount of interest accrued per year. It does not account for compounding interest.
APY (annual percentage yield) is a way of using the nominal interest rate to calculate the effective interest rate per year. It accounts for compounding interest.
EAR (effective annual rate) is a special type of APY that uses APR as the nominal interest rate.
Calculating the Yield of a Single-Period Investment
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Percent Change
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The Time Value of Money > Yield
The yield of an annuity may be found by discounting to find the PV, and then finding the percentage change from the PV to the FV.
The Internal Rate of Return (IRR) is the discount rate at which the NPV of an investment equals 0.
The IRR calculates an annualized yield of an annuity.
Calculating the Yield of an Annuity
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IRR Example
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The Time Value of Money > Yield
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Appendix
Key terms
accrue To add, or grow.
amortization The distribution of the cost of an intangible asset, such as an intellectual property right, over the projected useful life of the asset.
amortization schedule a table detailing each periodic payment over the life of the loan
amortized loan a form of debt where the principal is paid down over the life of the debt according to some amortization schedule, typically through equal payments
annuity A specified income payable at stated intervals for a fixed or a contingent period, often for the recipient’s life, in consideration of a stipulated premium paid either in prior installment payments or in a single payment. For example, a retirement annuity paid to a public officer following his or her retirement.
annuity-due An investment with fixed-payments that occur at regular intervals, paid at the beginning of each period.
annuity-due An annuity where the payments occur at the beginning of each period.
annuity-due a stream of fixed payments where payments are made at the beginning of each period
capitalization The process of finding the future value of a sum by evaluating the present value.
cash flow The sum of cash revenues and expenditures over a period of time.
compound interest Interest, as on a loan or a bank account, that is calculated on the total on the principal plus accumulated unpaid interest.
compound interest Interest, as on a loan or a bank account, that is calculated on the total on the principal plus accumulated unpaid interest.
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The Time Value of Money
compound interest Interest, as on a loan or a bank account, that is calculated on the total on the principal plus accumulated unpaid interest.
compounding period The length of time between the points at which interest is paid.
discount To find the value of a sum of money at some earlier point in time. To find the present value.
discount to account for the time value of money
discount rate The interest rate used to discount future cash flows of a financial instrument; the annual interest rate used to decrease the amounts of future cash flow to yield their present value.
discounting The process of finding the present value using the discount rate.
discounting The process of determining how much money paid/received in the future is worth today. You discount future values of cash back to the present using the discount rate.
discounting The process of finding the present value using the discount rate.
Effective Interest The amount of interest accrued per year after accounting for compounding.
effective-interest method amortizing a debt according to the effective interest rate paid
Future Value The value of an asset at a specific date. It measures the nominal future sum of money that a given sum of money is “worth” at a specified time in the future, assuming a certain interest rate, or more generally, rate of return, it is the present value multiplied by the accumulation function.
Future Value (FV) The value of the money in the future.
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The Time Value of Money
growth rate The percentage by which the payments grow each period.
incremental cash flows the additional money flowing in or out of a business due to a project
inflation An increase in the general level of prices or in the cost of living.
interest rate The percentage of an amount of money charged for its use per some period of time. It can also be thought of as the cost of not having money for one period, or the amount paid on an investment per year.
interest rate The percentage of an amount of money charged for its use per some period of time. It can also be thought of as the cost of not having money for one period, or the amount paid on an investment per year.
Interest Rate (i or r) The cost of not having money for one period, or the amount paid on an investment per year.
Internal Rate of Return (IRR) The discount rate that will cause the NPV of an investment to equal 0.
multi-period More than one unit of time.
Multi-period investment An investment that takes place over more than one periods.
net present value the present value of a project or an investment decision determined by summing the discounted incoming and outgoing future cash flows resulting from the decision
Net Present Value (NPV) The present value of a project or an investment decision determined by summing the discounted incoming and outgoing future cash flows resulting from the decision.
Nominal Interest The amount of interest accrued per year without accounting for compounding.
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The Time Value of Money
ordinary annuity An annuity where the payments occur at the end of each period.
ordinary annuity An investment with fixed-payments that occur at regular intervals, paid at the end of each period.
ordinary repair expense accrued in normal maintenance of an asset
period The length of time during which interest accrues.
period The length of time during which interest accrues.
period The length of time during which interest accrues.
Periods (t or n) Units of time. Usually one year.
perpetuity An annuity in which the periodic payments begin on a fixed date and continue indefinitely.
perpetuity An annuity in which the periodic payments begin on a fixed date and continue indefinitely.
present value Also known as present discounted value, is the value on a given date of a payment or series of payments made at other times. If the payments are in the future, they are discounted to reflect the time value of money and other factors such as investment risk. If they are in the past, their value is correspondingly enhanced to reflect that those payments have been (or could have been) earning interest in the intervening time. Present value calculations are widely used in business and economics to provide a means to compare cash flows at different times on a meaningful “like to like” basis.
present value a future amount of money that has been discounted to reflect its current value, as if it existed today
Present Value (PV) The value of the money today.
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The Time Value of Money
principal The money originally invested or loaned, on which basis interest and returns are calculated.
quarter A period of three consecutive months (1/4 of a year).
simple interest interest paid only on the principal.
Single-period investment An investment that takes place over one period, usually one year.
time period assumption business profit or loses are measured on timely basis
time value of money the value of an asset accounting for a given amount of interest earned or inflation accrued over a given period
yield In finance, the term yield describes the amount in cash that returns to the owners of a security. Normally it does not include the price variations, at the difference of the total return. Yield applies to various stated rates of return on stocks (common and preferred, and convertible), fixed income instruments (bonds, notes, bills, strips, zero coupon), and some other investment type insurance products
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The Time Value of Money
Simple Interest Formula
Simple interest is when interest is only paid on the amount you originally invested (the principal). You don’t earn interest on interest you previously earned.
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Wikipedia. “Future value.”
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The Time Value of Money
Compound Interest
Interest is paid at the total amount in the account, which may include interest earned in previous periods.
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Wikipedia. “Future value.”
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The Time Value of Money
Compounding Interest
The effect of earning 20% annual interest on an initial $1,000 investment at various compounding frequencies.
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Wikimedia.
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The Time Value of Money
Simple Interest Formula
Simple interest is when interest is only paid on the amount you originally invested (the principal). You don’t earn interest on interest you previously earned.
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Wikipedia. “Future value.”
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The Time Value of Money
Simple Interest Formula
Simple interest is when interest is only paid on the amount you originally invested (the principal). You don’t earn interest on interest you previously earned.
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Wikipedia. “Future value.”
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The Time Value of Money
Amortization Schedule
An example of an amortization schedule of a $100,000 loan over the first two years.
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Wikipedia. “Amortization schedule.”
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The Time Value of Money
Borrowing and lending
Banks like HSBC take such costs into account when determining the terms of a loan for borrowers.
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Geograph. “HSBC Bank Acocks Green 40-11-01 (C) Roy Hughes :: Geograph Britain and Ireland.”
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The Time Value of Money
IRR Example
The setup to find the IRR of the investment with cash flows of -4000, 1200, 1410, 1875, and 1050. By setting NPV = 0 and solving for r, you can find the IRR of this investment.
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Wikipedia. “Internal rate of return.”
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The Time Value of Money
Fisher Equation
The nominal interest rate is approximately the sum of the real interest rate and inflation.
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Wikipedia. “Fisher equation.”
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The Time Value of Money
Compound Interest
In this formula, your deposit ($100) is PV, i is the interest rate (5% for Bank 1, 6% for Bank 2), t is time (5 years), and FV is the future value.
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Wikipedia. “Future value.”
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The Time Value of Money
Compound Interest
Interest is paid at the total amount in the account, which may include interest earned in previous periods.
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Wikipedia. “Future value.”
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The Time Value of Money
Annual Percentage Yield
The Annual Percentage Yield is a way or normalizing the nominal interest rate. Basically, it is a way to account for the time factor in order to get a more accurate number for the actual interest rate.inom is the nominal interest rate.N is the number of compounding periods per year.
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Wikipedia. “Annual percentage yield.”
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The Time Value of Money
PV Annuity-due
The PV of an annuity with the payments at the beginning of each period
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Math Major.
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The Time Value of Money
FV Periodic Compounding
Finding the FV (A(t)) given the PV (Ao), nominal interest rate (r), number of compounding periods per year (n), and number of years (t).
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Wikipedia. “Compound interest.”
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The Time Value of Money
Present Value Single Payment
Finding the PV is a matter of plugging in for the three other variables.
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Wikipedia. “Time value of money.”
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The Time Value of Money
Simple Interest Formula
Simple interest is when interest is only paid on the amount you originally invested (the principal). You don’t earn interest on interest you previously earned.
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Wikipedia. “Future value.”
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The Time Value of Money
Percent Change
The percent change in value is the change in value from PV to FV (V2 to V1) divided by PV (V1) times 100%.
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Wikipedia. “Percentage change.”
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The Time Value of Money
FV of a single payment
The PV and FV are directly related.
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Wikipedia. “Time value of money.”
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The Time Value of Money
Solving for n
This formula allows you to figure out how many periods are needed to achieve a certain future value, given a present value and an interest rate.
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Wikipedia. “Compound interest.”
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The Time Value of Money
Calculating the effective annual rate
The effective annual rate for interest that compounds more than once per year.
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The Time Value of Money
Simple Interest Formula
Simple interest is when interest is only paid on the amount you originally invested (the principal). You don’t earn interest on interest you previously earned.
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Wikipedia. “Future value.”
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The Time Value of Money
Sum FV
The PV of an investment is the sum of the present values of all its payments.
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The Time Value of Money
Car
Car loans, mortgages, and student loans all generally have compound interest.
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The Time Value of Money
Compound Interest
Interest is paid at the total amount in the account, which may include interest earned in previous periods.
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Wikipedia. “Future value.”
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The Time Value of Money
EAR
The Effective Annual Rate is the amount of interest actually accrued per year based on the APR. n is the number of compounding periods of APR per year.
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Wikipedia. “Effective APR.”
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The Time Value of Money
FV Ordinary Annuity
The FV of an annuity with the payments at the end of each period
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http://fonetika3.appspot.com/wiki/Time_value_of_money#Present_value_of_a_future_sum.
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The Time Value of Money
FV Annuity-Due
The FV of an annuity with payments at the beginning of each period: m is the amount amount, r is the interest, n is the number of periods per year, and t is the number of years.
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Connexions. “Mathematics of Finance.”
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The Time Value of Money
FV of a single payment
The FV of multiple cash flows is the sum of the future values of each cash flow.
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The Time Value of Money
PV Ordinary Annuity
The PV of an annuity with the payments at the end of each period
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The Time Value of Money
FV of a single payment
The PV and FV are directly related.
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The Time Value of Money
PV of a Perpetuity
The PV of a perpetuity is the payment size divided by the interest rate.
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The Time Value of Money
EAR with Continuous Compounding
The effective rate when interest compounds continuously.
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The Time Value of Money
FV of a single payment
The FV is related to the PV by being i% more each period.
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The Time Value of Money
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The Time Value of Money
Which of these is a variable used to calculate the time value of money?
A) The interest rate.
B) The amount of time that has passed.
C) The present value of the sum you have.
D) All of these answers.
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The Time Value of Money
Which of these is a variable used to calculate the time value of money?
A) The interest rate.
B) The amount of time that has passed.
C) The present value of the sum you have.
D) All of these answers.
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The Time Value of Money
Which of the following is an explanation for why the concept of the time value of money is important to a business?
A) The present value of a dollar you get in a year is less than the value of a dollar you get today.
B) By figuring out the present value of future income, a company can better compare possible projects.
C) A project’s future unadjusted revenues can be misleading when trying to determine its profitability.
D) All of these answers.
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The Time Value of Money
Which of the following is an explanation for why the concept of the time value of money is important to a business?
A) The present value of a dollar you get in a year is less than the value of a dollar you get today.
B) By figuring out the present value of future income, a company can better compare possible projects.
C) A project’s future unadjusted revenues can be misleading when trying to determine its profitability.
D) All of these answers.
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The Time Value of Money
You have $300,000 that you want to invest in a one year Certificate of Deposit (CD) with a 4% annual interest rate. What will be the value of that CD in a year?
A) $420,000
B) $301,200
C) $312,000
D) $315,000
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The Time Value of Money
You have $300,000 that you want to invest in a one year Certificate of Deposit (CD) with a 4% annual interest rate. What will be the value of that CD in a year?
A) $420,000
B) $301,200
C) $312,000
D) $315,000
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The Time Value of Money
What is the future value in 30 years of $100,000 invested today in a savings account earning a 1% compound interest rate every year (rounded up to the nearest dollar)?
A) 30000
B) 130000
C) More than $134785
D) 134785
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The Time Value of Money
What is the future value in 30 years of $100,000 invested today in a savings account earning a 1% compound interest rate every year (rounded up to the nearest dollar)?
A) 30000
B) 130000
C) More than $134785
D) 134785
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The Time Value of Money
You plan to invest $100,000 in a 3 year Certificate of Deposit that has a 5% compound interest rate. What is its future value?
A) $115,763
B) $115,000
C) $105,000
D) $115,927
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The Time Value of Money
You plan to invest $100,000 in a 3 year Certificate of Deposit that has a 5% compound interest rate. What is its future value?
A) $115,763
B) $115,000
C) $105,000
D) $115,927
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The Time Value of Money
You plan to invest $100,000 in a 3 year Certificate of Deposit that has a simple interest rate of 5%. What is its future value?
A) $115,763
B) $105,000
C) $115,000
D) $115,927
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The Time Value of Money
You plan to invest $100,000 in a 3 year Certificate of Deposit that has a simple interest rate of 5%. What is its future value?
A) $115,763
B) $105,000
C) $115,000
D) $115,927
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The Time Value of Money
The future value concept answers which of the following questions?
A) How much money will you have in 10 years if you invest $10,000 today earning 10% as interest every year?
B) How much money will you have in 10 years if you invest $10,000 every year at 10% interest every year?
C) All of these answers
D) How much money will you have in 10 years if you invest $10,000 every year at 10% net return?
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The Time Value of Money
The future value concept answers which of the following questions?
A) How much money will you have in 10 years if you invest $10,000 today earning 10% as interest every year?
B) How much money will you have in 10 years if you invest $10,000 every year at 10% interest every year?
C) All of these answers
D) How much money will you have in 10 years if you invest $10,000 every year at 10% net return?
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The Time Value of Money
Which of the following is the correct formula for calculating future value with simple interest?
A) FV = PV * (1+i)t
B) FV = PV * i
C) All of these answers
D) FV = PV * (1+i*t)
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The Time Value of Money
Which of the following is the correct formula for calculating future value with simple interest?
A) FV = PV * (1+i)t
B) FV = PV * i
C) All of these answers
D) FV = PV * (1+i*t)
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The Time Value of Money
What is the future value in 30 years of $100,000 invested today in a savings account earning a 1% simple interest rate every year (rounded up to the nearest dollar)?
A) 130,000
B) 30,000
C) 134,785
D) More than $134,785
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The Time Value of Money
What is the future value in 30 years of $100,000 invested today in a savings account earning a 1% simple interest rate every year (rounded up to the nearest dollar)?
A) 130,000
B) 30,000
C) 134,785
D) More than $134,785
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The Time Value of Money
A period of three consecutive months (1/4 of a year).
A) quarter
B) Discounting
C) perpetuity
D) annuity
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The Time Value of Money
A period of three consecutive months (1/4 of a year).
A) quarter
B) Discounting
C) perpetuity
D) annuity
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The Time Value of Money
You decide to make an investment on a bond that pays 5% interest on the principal only. Which of the following describes how interest accrues on this investment?
A) Compound interest.
B) Incepted interest.
C) Simple interest.
D) All of these answers.
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The Time Value of Money
You decide to make an investment on a bond that pays 5% interest on the principal only. Which of the following describes how interest accrues on this investment?
A) Compound interest.
B) Incepted interest.
C) Simple interest.
D) All of these answers.
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The Time Value of Money
In a year, you expect to receive a payment of $1 million in a year. That annual interest rate is 5%. What is the present value of the future payment?
A) $666,667
B) $952,381
C) $995,025
D) $1,050,000
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The Time Value of Money
In a year, you expect to receive a payment of $1 million in a year. That annual interest rate is 5%. What is the present value of the future payment?
A) $666,667
B) $952,381
C) $995,025
D) $1,050,000
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The Time Value of Money
What is the present value of $100,000 that will be received 5 years from today if you face a 10% compound interest rate every year (rounded up to the nearest dollar)?
A) 62092
B) 52092
C) 72092
D) 82092
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The Time Value of Money
What is the present value of $100,000 that will be received 5 years from today if you face a 10% compound interest rate every year (rounded up to the nearest dollar)?
A) 62092
B) 52092
C) 72092
D) 82092
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The Time Value of Money
Assume you invest money in a bond that will pay you $250,000 in four years. The bond has an annual interest rate of 5%. You do not receive interest payments while you own the bond; it is zero-coupon. What is the bond’s present value?
A) $205,676
B) $205,482
C) $238,095
D) $240,385
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The Time Value of Money
Assume you invest money in a bond that will pay you $250,000 in four years. The bond has an annual interest rate of 5%. You do not receive interest payments while you own the bond; it is zero-coupon. What is the bond’s present value?
A) $205,676
B) $205,482
C) $238,095
D) $240,385
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The Time Value of Money
Which of the following is a cost to the investor that is included in the calculation of an investment’s interest rate?
A) Opportunity Cost.
B) Inflation.
C) Risk of a bad investment.
D) All of these answers.
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The Time Value of Money
Which of the following is a cost to the investor that is included in the calculation of an investment’s interest rate?
A) Opportunity Cost.
B) Inflation.
C) Risk of a bad investment.
D) All of these answers.
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The Time Value of Money
Which of the following could be an appropriate period used in a present value calculation?
A) A year.
B) A month.
C) Three months.
D) All of these answers.
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The Time Value of Money
Which of the following could be an appropriate period used in a present value calculation?
A) A year.
B) A month.
C) Three months.
D) All of these answers.
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The Time Value of Money
Which of the following the correct formula for calculating present value using compound interest?
A) PV = FV/(1+(i*t))
B) PV = FV/(i)
C) All of these answers.
D) PV = FV / (1+i)n
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The Time Value of Money
Which of the following the correct formula for calculating present value using compound interest?
A) PV = FV/(1+(i*t))
B) PV = FV/(i)
C) All of these answers.
D) PV = FV / (1+i)n
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The Time Value of Money
A security offers to pay the holder $1000 at the end of every month for five years. What type of annuity is this?
A) Annuity-due.
B) Ordinary annuity.
C) Perpetuity.
D) Regular annuity.
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The Time Value of Money
A security offers to pay the holder $1000 at the end of every month for five years. What type of annuity is this?
A) Annuity-due.
B) Ordinary annuity.
C) Perpetuity.
D) Regular annuity.
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The Time Value of Money
An annuity pays $1500 at the beginning of every month for five years. The interest rate of the annuity is 4%. What is this annuity’s future value?
A) $97,948
B) $99,448
C) $101,280
D) $99,780
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The Time Value of Money
An annuity pays $1500 at the beginning of every month for five years. The interest rate of the annuity is 4%. What is this annuity’s future value?
A) $97,948
B) $99,448
C) $101,280
D) $99,780
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The Time Value of Money
A five year annuity pays $1000 at the end of every month for four years. It has an interest rate of 3%. What is its present value?
A) $3,717
B) $26,024
C) $3,828
D) $25,266
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The Time Value of Money
A five year annuity pays $1000 at the end of every month for four years. It has an interest rate of 3%. What is its present value?
A) $3,717
B) $26,024
C) $3,828
D) $25,266
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The Time Value of Money
A person purchases a security that pays $1000 a year in perpetuity. The interest rate of that security is 4%. What is the present value of that security?
A) $25,000
B) $1040
C) $250,000
D) $4160
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The Time Value of Money
A person purchases a security that pays $1000 a year in perpetuity. The interest rate of that security is 4%. What is the present value of that security?
A) $25,000
B) $1040
C) $250,000
D) $4160
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The Time Value of Money
The sum of cash revenues and expenditures over a period of time.
A) Cash
B) Cash Flow
C) Assets
D) Account Receivables
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The Time Value of Money
The sum of cash revenues and expenditures over a period of time.
A) Cash
B) Cash Flow
C) Assets
D) Account Receivables
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The Time Value of Money
You purchase two annuities. The first is for three years and pays $1500 annually. The second is for four years and pays $2000 annually. The interest rate for both is 4%. What is the Future Value of this portfolio?
A) $12,612.90
B) $13,175.33
C) $506.74
D) $485.11
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The Time Value of Money
You purchase two annuities. The first is for three years and pays $1500 annually. The second is for four years and pays $2000 annually. The interest rate for both is 4%. What is the Future Value of this portfolio?
A) $12,612.90
B) $13,175.33
C) $506.74
D) $485.11
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The Time Value of Money
You can purchase two three-year annuities today. One is valued at $2000, the other at $4000. The 1st annuity begins paying $1000 in a year. The 2nd annuity begins paying $1500 in two years. The interest rate is 5%. What is the PV of the portfolio?
A) $613.60
B) $6613.60
C) $808.12
D) $6808.12
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The Time Value of Money
You can purchase two three-year annuities today. One is valued at $2000, the other at $4000. The 1st annuity begins paying $1000 in a year. The 2nd annuity begins paying $1500 in two years. The interest rate is 5%. What is the PV of the portfolio?
A) $613.60
B) $6613.60
C) $808.12
D) $6808.12
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The Time Value of Money
Of the following car financing options, which one would you prefer while assuming that you prefer paying the least amount of dollars and that you face a 10% annual compound interest rate on all your financial decisions?
A) A lump-sum payment of $20,000 in two years from today.
B) A payment $10,000 today and another of $10,000 in one year from today.
C) A lump-sum payment of $19,000 today only.
D) A lump-sum payment of $20,000 today only.
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The Time Value of Money
Of the following car financing options, which one would you prefer while assuming that you prefer paying the least amount of dollars and that you face a 10% annual compound interest rate on all your financial decisions?
A) A lump-sum payment of $20,000 in two years from today.
B) A payment $10,000 today and another of $10,000 in one year from today.
C) A lump-sum payment of $19,000 today only.
D) A lump-sum payment of $20,000 today only.
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The Time Value of Money
Which of the following describes the relationship between present value and future value?
A) When present value increases, the future value decreases, assuming all variables are constant.
B) When one increases, the other increases, assuming all variables are constant.
C) The higher the interest rate, the higher the present value and the lower the future value.
D) The more time that passes, the higher the present value and the lower the future value.
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The Time Value of Money
Which of the following describes the relationship between present value and future value?
A) When present value increases, the future value decreases, assuming all variables are constant.
B) When one increases, the other increases, assuming all variables are constant.
C) The higher the interest rate, the higher the present value and the lower the future value.
D) The more time that passes, the higher the present value and the lower the future value.
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The Time Value of Money
You own a perpetuity that pays $1000 annually. It has a 5% annual interest rate and a 2% annual growth rate. What is the present value of the perpetuity?
A) $20,000
B) $33,333
C) $50,000
D) $14,286
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The Time Value of Money
You own a perpetuity that pays $1000 annually. It has a 5% annual interest rate and a 2% annual growth rate. What is the present value of the perpetuity?
A) $20,000
B) $33,333
C) $50,000
D) $14,286
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The Time Value of Money
A bond currently valued at $100,000 has a quarterly interest rate of 5%. The bond matures in 3 years. What is its future value?
A) $1,157,625
B) $1,219,391
C) $1,160,755
D) $1,050,945
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The Time Value of Money
A bond currently valued at $100,000 has a quarterly interest rate of 5%. The bond matures in 3 years. What is its future value?
A) $1,157,625
B) $1,219,391
C) $1,160,755
D) $1,050,945
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The Time Value of Money
Which of the following is a definition for the term “real interest rate”?
A) The rate of return that capital could earn in an alternative investment of equivalent risk.
B) The amount of interest actually accrued in a given period.
C) All of these answers.
D) The interest rate accrued after accounting for inflation.
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The Time Value of Money
Which of the following is a definition for the term “real interest rate”?
A) The rate of return that capital could earn in an alternative investment of equivalent risk.
B) The amount of interest actually accrued in a given period.
C) All of these answers.
D) The interest rate accrued after accounting for inflation.
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The Time Value of Money
Which of the following is a definition for cost of capital?
A) The rate of return that capital could earn in an alternative investment of equivalent risk.
B) The interest rate accrued after accounting for inflation.
C) The amount of interest actually accrued in a given period.
D) All of these answers.
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The Time Value of Money
Which of the following is a definition for cost of capital?
A) The rate of return that capital could earn in an alternative investment of equivalent risk.
B) The interest rate accrued after accounting for inflation.
C) The amount of interest actually accrued in a given period.
D) All of these answers.
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The Time Value of Money
You purchase a three year certificate of deposit (CD) for $100,000 on January 1st, 2000. This CD has an annual interest rate of 5%. The interest compounds continuously. What is the balance for the CD account on July 1, 2001?
A) $107,593
B) $105,000
C) $107,500
D) $110,250
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The Time Value of Money
You purchase a three year certificate of deposit (CD) for $100,000 on January 1st, 2000. This CD has an annual interest rate of 5%. The interest compounds continuously. What is the balance for the CD account on July 1, 2001?
A) $107,593
B) $105,000
C) $107,500
D) $110,250
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The Time Value of Money
Which of the following statements about the amortization of a loan is true?
A) A loan is fully amortized once the amortization schedule is drafted.
B) Amortization is the process of paying off a debt over time through regular payments.
C) 50% of each payment is for interest while the rest is applied to the principal balance.
D) All of these answers.
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The Time Value of Money
Which of the following statements about the amortization of a loan is true?
A) A loan is fully amortized once the amortization schedule is drafted.
B) Amortization is the process of paying off a debt over time through regular payments.
C) 50% of each payment is for interest while the rest is applied to the principal balance.
D) All of these answers.
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The Time Value of Money
Which of the following correctly defines a method of determining a single period investment’s yield?
A) The Effective Annual rate is the interest rate multiplied by the number of payment periods per year.
B) Annual Percentage Rate = (1+(i/N))^N – 1.
C) Change-in-value equals the investment’s FV minus its PV. Divide that by PV and multiply by 100%.
D) All of these answers.
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The Time Value of Money
Which of the following correctly defines a method of determining a single period investment’s yield?
A) The Effective Annual rate is the interest rate multiplied by the number of payment periods per year.
B) Annual Percentage Rate = (1+(i/N))^N – 1.
C) Change-in-value equals the investment’s FV minus its PV. Divide that by PV and multiply by 100%.
D) All of these answers.
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The Time Value of Money
You purchase a two year annuity for $2800. The annuity pays $1500 each year. What is the annuity’s approximate IRR?
A) 8.6%
B) 4.5%
C) 2.3%
D) 10%
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The Time Value of Money
You purchase a two year annuity for $2800. The annuity pays $1500 each year. What is the annuity’s approximate IRR?
A) 8.6%
B) 4.5%
C) 2.3%
D) 10%
Attribution
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//finance/definition/discount
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//finance/definition/discounting–2
Wiktionary. “discount rate.”
CC BY-SA 3.0
http://en.wiktionary.org/wiki/discount+rate
Wikipedia. “Cost of capital.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Cost_of_capital
Wikipedia. “Discounting.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Discounting
Wikipedia. “Future value.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Future_value
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//finance/definition/multi-period-investment
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//finance/definition/single-period-investment
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//finance/definition/periods-t-or-n
Connexions. “Mathematics of Finance.”
CC BY 3.0
http://cnx.org/content/m18905/latest/
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//finance/definition/ordinary-annuity–2
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//finance/definition/annuity-due–2
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//accounting/definition/ordinary-repair
Wikipedia. “Future value.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Future_value
Wikipedia. “Future value.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Future_value
Wiktionary. “compound interest.”
CC BY-SA 3.0
http://en.wiktionary.org/wiki/compound+interest
Wikipedia. “Present value.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Present_value
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Wiktionary. “simple interest.”
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http://en.wiktionary.org/wiki/simple+interest
Wiktionary. “compound interest.”
CC BY-SA 3.0
http://en.wiktionary.org/wiki/compound+interest
Wikipedia. “Cost of capital.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Cost_of_capital
Wikipedia. “Fisher equation.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Fisher_equation
Wiktionary. “inflation.”
CC BY-SA 3.0
http://en.wiktionary.org/wiki/inflation
Wikipedia. “Compound interest.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Compound_interest
Wikipedia. “Compound interest.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Compound_interest
Wikipedia. “Accounting assumptions.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Accounting_assumptions
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//finance/definition/compounding-period
Wikipedia. “time value of money.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/time%20value%20of%20money
Wikipedia. “Loan.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Loan
http://loanhr.com/loan-amortization/meaning-of-loan-amortization-and-its-requirement/.
CC BY
http://loanhr.com/loan-amortization/meaning-of-loan-amortization-and-its-requirement/
Wikipedia. “Amortization schedule.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Amortization_schedule
Wikipedia. “Amortizing loan.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Amortizing_loan
Wiktionary. “amortization.”
CC BY-SA 3.0
http://en.wiktionary.org/wiki/amortization
Wikipedia. “Amortization schedule.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Amortization_schedule
Wikipedia. “Amortization (business).”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Amortization_(business)
Wikipedia. “Future value.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Future_value
Wiktionary. “accrue.”
CC BY-SA 3.0
http://en.wiktionary.org/wiki/accrue
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Wiktionary. “principal.”
CC BY-SA 3.0
http://en.wiktionary.org/wiki/principal
Connexions. “Mathematics of Finance.”
CC BY 3.0
http://cnx.org/content/m18905/latest/
Wikibooks. “Principles of Finance/Section 1/Chapter 3/Applications of Time Value of Money/Annuities.”
CC BY-SA 3.0
http://en.wikibooks.org/wiki/Principles_of_Finance/Section_1/Chapter_3/Applications_of_Time_Value_of_Money/Annuities
Wiktionary. “perpetuity.”
CC BY-SA 3.0
http://en.wiktionary.org/wiki/perpetuity
Wikipedia. “Perpetuity.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Perpetuity
Wikipedia. “Present value.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Present_value
Wikipedia. “Present value.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Present_value
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//finance/definition/discounting–2
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//finance/definition/capitalization
Wikipedia. “Future value.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Future_value
Wikipedia. “Terminal value (finance).”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Terminal_value_(finance)
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//finance/definition/growth-rate
Wikipedia. “Time value of money.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Time_value_of_money
Wikipedia. “Perpetuities.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Perpetuities
Wikipedia. “Internal rate of return.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Internal_rate_of_return
Wikipedia. “Annual percentage rate.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Annual_percentage_rate
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//accounting/definition/effective-interest-method
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//finance/definition/effective-interest
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//finance/definition/nominal-interest
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Wikipedia. “Annual percentage yield.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Annual_percentage_yield
Wikipedia. “Yield (finance).”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Yield_(finance)
Wikipedia. “Future value.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Future_value
Wiktionary. “quarter.”
CC BY-SA 3.0
http://en.wiktionary.org/wiki/quarter
Wikipedia. “Present value.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Present_value
Wikipedia. “period.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/period
Wikipedia. “Time value of money.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Time_value_of_money
Wikipedia. “Annuity (finance theory).”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Annuity_(finance_theory)
Wikipedia. “Cash flow.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Cash_flow
Wiktionary. “annuity.”
CC BY-SA 3.0
http://en.wiktionary.org/wiki/annuity
Wiktionary. “cash flow.”
CC BY-SA 3.0
http://en.wiktionary.org/wiki/cash+flow
Wikibooks. “Principles of Finance/Section 1/Chapter 2/Time Value of Money/Introduction.”
CC BY-SA 3.0
http://en.wikibooks.org/wiki/Principles_of_Finance/Section_1/Chapter_2/Time_Value_of_Money/Introduction
Wikipedia. “Time value of money.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Time_value_of_money
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//finance/definition/interest-rate-i-or-r
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//finance/definition/future-value-fv
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//finance/definition/present-value-pv
Wikipedia. “Annuity (finance theory).”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Annuity_(finance_theory)
Wikipedia. “Annuity (finance theory).”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Annuity_(finance_theory)
Wikipedia. “Internal rate of return.”
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http://en.wikipedia.org/wiki/Internal_rate_of_return
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Wiktionary. “yield.”
CC BY-SA 3.0
http://en.wiktionary.org/wiki/yield
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//finance/definition/net-present-value-npv
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//finance/definition/internal-rate-of-return-irr
Wikipedia. “Present value.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Present_value
Wiktionary. “interest rate.”
CC BY-SA 3.0
http://en.wiktionary.org/wiki/interest+rate
Wikipedia. “period.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/period
Wiktionary. “compound interest.”
CC BY-SA 3.0
http://en.wiktionary.org/wiki/compound+interest
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//finance/definition/multi-period
http://fonetika3.appspot.com/wiki/Time_value_of_money#Present_value_of_a_future_sum.
CC BY-SA
http://fonetika3.appspot.com/wiki/Time_value_of_money#Present_value_of_a_future_sum
Wikipedia. “Net present value.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Net_present_value
Wikipedia. “Time value of money.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Time_value_of_money
Wiktionary. “net present value.”
CC BY-SA 3.0
http://en.wiktionary.org/wiki/net+present+value
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//finance/definition/discount
Wikipedia. “Compound interest.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Compound_interest
Wikipedia. “Effective annual rate.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Effective_annual_rate
Wikipedia. “Effective annual rate.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Effective_annual_rate
Wikipedia. “Future Value.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Future%20Value
Wikipedia. “Present value.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Present_value
Wikipedia. “Time value of money.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Time_value_of_money
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Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//finance/definition/discounting–2
Wiktionary. “interest rate.”
CC BY-SA 3.0
http://en.wiktionary.org/wiki/interest+rate
Connexions. “Mathematics of Finance.”
CC BY 3.0
http://cnx.org/content/m18905/latest/
Wikipedia. “Annuity (finance theory).”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/Annuity_(finance_theory)
Wikipedia. “period.”
CC BY-SA 3.0
http://en.wikipedia.org/wiki/period
Wiktionary. “perpetuity.”
CC BY-SA 3.0
http://en.wiktionary.org/wiki/perpetuity
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//finance/definition/ordinary-annuity–2
Boundless Learning. “Boundless.”
CC BY-SA 3.0
http://www.boundless.com//finance/definition/annuity-due–2
http://fonetika3.appspot.com/wiki/Time_value_of_money#Present_value_of_a_future_sum.
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