Question

Problem 4: Find the numerical value of (FA, 19%,20) by (a) linear interpolation, (b) using the appropriate formula, and (c) a spreadsheet function.

Answer 1

The objective of the following analysis is to obtain the numerical value of (F/A, 19% ,20) by using three methods.

(a) Linear interpolation

It shall be noted that under this method, (F/A,19%,20) is obtained by interpolating between i=18% and i=20% at n=20

It shall further be noted that (F/A,18%,20)=146.6280 and (F/A,20%,20)=186.6880

That means,

Thus, (F/A,19%,20)=(F/A,18%,20)+20.03 = 146.6280+20.03 = 166.658

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(b) Using approximation formula

The result is:

i=19%, n=20

Thus, (F/A, 19%, 20) = 165.418

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(c) Using spreadsheet function

i=19%, n=20

Assume, FV=F=1, PV=P=0, Type=0

Use formula =-PMT(i,n,P,F,Type) to compute A and then compute F/A

A=-PMT(19%,20,0,1,0) = 0.00604529

Hence, F/A=1/0.00604529=165.418018

Hence, (F/A,19%,20)=165.418018