10.12 Interpolation Illustrated

Interpolation may be useful in order to estimate future (and present-) values when one does not wish, or have the ability, to calculate more precise measures. The reason for the error has to do with the curvilinear relationship between (discount- and) compound interest rates and their related multipliers. This is best seen by illustration. 

 

One may readily see that, by connecting the asterisks, the interpolated value of 2.4806 resides on a straight line between the correctly calculated future value multipliers for 9% and 10% respectively.

However, the time value of money is not linear. Any time an exponent is involved, you will not get a linear relationship, but a curvilinear outcome of some sort. Hence, the correct multiplier for 9.5% is 2.4782, which is lower than the interpolated arithmetic average of 2.4806. If one joins the asterisks for 9% and 10% to the mathematically calculated middle value of 2.4782 (represented by “#”), one readily observes the curvilinear relationship between compound interest rates and their respective multipliers. In short, as rates increase, future values increase in non-linear fashion. Correspondingly, present values would decrease non-linearly. The non-linear nature of these curves will soon be discussed in greater depth when we get to “Volatility.” Basic mathematical examples will be presented.

License

Icon for the Creative Commons Attribution 4.0 International License

Introduction to Financial Analysis Copyright © 2022 by Kenneth S. Bigel is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

Share This Book