Time Value of Money
Introduction
Time Value of Money (TVM) is an important concept in financial management. It can be
used to compare investment alternatives and to solve problems involving loans, mortgages,
leases, savings, and annuities.
TVM is based on the concept that a dollar that you have today is worth more than the
promise or expectation that you will receive a dollar in the future. Money that you hold
today is worth more because you can invest it and earn interest. After all, you should
receive some compensation for foregoing spending. For instance, you can invest your dollar
for one year at a 6% annual interest rate and accumulate $1.06 at the end of the
year. You can say that the future value of the dollar is $1.06
given a 6% interest rate and a oneyear period. It
follows that the present value of the $1.06 you expect to receive in one
year is only $1.
A key concept of TVM is that a single sum of money or a series of equal, evenlyspaced
payments or receipts promised in the future can be converted to an equivalent value
today. Conversely, you can determine the value to which a single sum or a series of
future payments will grow to at some future date.
You can calculate the fifth value if you are given any four of: Interest Rate, Number
of Periods, Payments, Present Value, and Future Value. Each of these factors is very
briefly defined in the righthand column below. The left column has references to
more detailed explanations, formulas, and examples.

Interest is a charge for borrowing money, usually stated as a percentage of the amount
borrowed over a specific period of time. Simple interest is
computed only on the original amount borrowed. It is the return on that principal for one
time period. In contrast, compound interest is calculated each
period on the original amount borrowed plus all unpaid interest
accumulated to date. Compound interest is always assumed in TVM problems. 

Periods are evenlyspaced intervals of time. They are intentionally not stated in
years since each interval must correspond to a compounding period for a single amount or a
payment period for an annuity. 

Payments are a series of equal, evenlyspaced cash flows. In TVM applications,
payments must represent all outflows (negative amount) or all inflows (positive amount). 

Present Value is an amount today that is equivalent to a future
payment, or series of payments, that has been discounted by an appropriate interest
rate. The future amount can be a single sum that will be received at the end of the
last period, as a series of equallyspaced payments (an annuity), or both. Since
money has time value, the present value of a promised future amount is worth less the
longer you have to wait to receive it. 

Future Value is the amount of money that an investment
with a fixed, compounded interest rate will grow to by some future date. The investment
can be a single sum deposited at the beginning of the first period, a series of
equallyspaced payments (an annuity), or both. Since money has time value, we
naturally expect the future value to be greater than the present value. The difference
between the two depends on the number of compounding periods involved and the going
interest rate. 

A method for repaying a loan in equal installments. Part of each payment goes toward
interest and any remainder is used to reduce the principal. As the balance of the loan is gradually reduced, a
progressively larger portion of each payment goes toward reducing principal. 

A cash flow diagram is a picture of a financial problem that shows all
cash inflows and outflows along a time line. It can help you to visualize a problem
and to determine if it can be solved by TVM methods. 
References:
Gallager, T; Andrew Jr., J., Financial
Management: Principals and Practices, Upper Saddle River, NJ: Prentice Hall, 1996
Kieso, D; Weygandt, Jerry, Intermediate
Accounting, 9^{th} Ed., New York, NY:John Wiley & Sons, Inc., 1993
BA II Plus Guidebook, Texas Instruments, Inc., 1996
HP10B Business Calculator Owner's Manual, Hewlett Packard, 1994

