## 49 Special Problems

4.9.1 Introduction

The preceding sections of this chapter outline an approach for conducting deterministic economic analysis of investment opportunities. Adherence to the concepts and methods presented will lead to sound investment decisions with respect to time value of money principles. This section addresses several topics that are of special interest in some analysis situations.

### 4.9.2 Interpolating Interest Tables

All of the examples previously presented in this chapter conveniently used interest rates whose time value of money factors were tabulated in Appendix 4A. How does one proceed if non-tabulated time value of money factors are needed? There are two viable approaches; calculation of the exact values and interpolation. The best and theoretically correct approach is to calculate the exact values of needed factors based on the formulas in Table 4.6.

Example 22

Determine the exact value for (FIP,13%,7).

From Table 4.6,

Interpolation is often used instead of calculation of exact values because, with practice, interpolated values can be calculated quickly. Interpolated values are not "exact" but for most practical problems they are "close enough," particularly if the range of interpolation is kept as narrow as possible. Interpolation of some factors, for instance (PIA,i,n), also tends to be less error prone than the exact calculation due simpler mathematical operations.

Interpolation involves determining an unknown time value of money factor using two known values which bracket the value of interest. An assumption is made that the values of the time value of money factor vary linearly between the known values. Ratios are then used to estimate the unknown value. The example below illustrates the process.

Example 23

Determine an interpolated value for (FIP,13%,7).

The narrowest range of interest rates which bracket 13% and for which time value of money factor tables are provided in Appendix 4A is 12% to 15%.

The values necessary for this interpolation are

 i values (FI P,i%,7) 12%
0 0