# Econ

3040 Words13 Pages
KEATMX01_p001-008.qxd

11/2/12

2:22 PM

Page 1

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
2

Managerial Economics

KEATMX01_p001-008.qxd

11/2/12

2:22 PM

Page 3

T HE F UTURE VALUE
Module
3A

OF AN

A NNUITY

In the previous section, we deal with the compounding of a single sum. But suppose a uniform amount is set aside each period (e.g., each year), and we want to know how much will be in the account after several years.
For example, suppose five annual deposits of \$500 each will be made to an account paying 7 percent annually, starting 1 year from now. What will be the amount at the end of 5 years? A simple diagram will illustrate:
FVa ϭ ?
500
0

500

500

500

500

1

2

3

4

5

The first \$500 will collect interest for 4 years, the second for 3 years, and so on. This problem could be solved by making all the separate calculations and adding the items:
FVa ϭ A (1 ϩ i )nϪ1 ϩ A (1 ϩ i)nϪ2 ϩ · · · ϩ A (1 ϩ i )0

where FVa ϭ Future value of the annuity
A ϭ Annuity
This expression simplifies to
(1 + i )n − 1 i Again, a table has been constructed to ease the effort involved in this calculation.
Table A.1b in Appendix A shows the sum of an annuity. For the question posed here the answer is:
FVa ϭ A (Factor) ϭ 500 (5.7507) ϭ 2,875.35

where “factor” is found in Table A.1b.
The preceding calculation solves for the future value of the annuity. But suppose we have a problem stated in the following form:
To finance the college education of a just-born child, the