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Calculations for Time
Value of Money
TVM

In this appendix, a brief explanation of the computation of the time value of money is given for readers not familiar with this subject. Modern technology has made these calculations very easy. Many computer programs have built-in time-value functions, and a large assortment of handheld calculators will solve these problems using special keys. However, some people who use these methods do not understand the rationale for the answers and merely accept the results.
At the other extreme, the calculations could be made using exponentials and/or logarithms. Such a procedure may provide a thorough learning experience, but it is tedious and time consuming. Compound interest tables have been developed to provide a relatively easy tool for solving time-value problems. They are found in
Appendix A at the end of the textbook. Here we walk through four types of calculations, each representing one of the four tables.
The Excel icons marked TVM refer to the Excel spreadsheets that can be found on the companion web site.

T HE F UTURE VALUE

OF A

S INGLE S UM

Module If you deposit $1,000 in a savings account that pays 7 percent interest annually, and
3A
you do not withdraw this interest, the original amount will keep growing. (In real

life, bank interest is usually compounded more frequently than once per year, but annual compounding is assumed here. In other words, the 7 percent will be credited to the account once per year, at the end of the year.) One year later, $70 of interest will be added to the account, making the total balance $1,070. In mathematical terms, this occurrence can be written as follows: if i equals the annual interest rate, then the amount of interest paid in one year equals A times i, where A is the original amount
deposited.