Chapter 4, Problem 21P

To determine

Interest Rate.

Answer to Problem 21P

7.242% is the interest rate.

Explanation of Solution

Given information:

Using linear interpolation, values to be found for (F/A,11%,15) and (F/P,16%,25).

With this problem, start with the interpolation exercise. Here, the goal is to try to find the interest rate from information that is available to us. Since the interest rate is not known for 6.25% but for 6.00% and 7.00%, split the difference to try to get the amount. Located below are the two values for the available information:

(P/A,6.00%,10%)=7.360

AND

(P/A,7.00%,10)=7.024

As of the result, apply the interpolation formula this can be seen as below:

$(P/A,6\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\%,10)=\frac{1}{2}\left[\begin{array}{l}(AnnuityFactorofthelower\lim it)-\\ (AnnuityFactoroftheUpperLimit\end{array}\right]$

$+(AnnuityFactoroftheupperLimit)$

$=\frac{1}{2}\left[(P/A,6\%,10)-(P/A,7\%,10)\right]+(P/A,7\%,10)$

$=\frac{1}{2}(7.360-7.024)+7.024$

$=\frac{1}{2}(0336)+7.024$

$=0.168+7.024$

$=7.192$

Thus, by using the interest tables and linear interpolation, the end result for this part of the problem is a factor of 7.192.

Now, apply the TVM calculator that is needed for the second part of the problem. There are a number of ways that one can do this first option is a financial calculator a second option is the use of an online calculator.

To expedite the comparison between the two, the end result of our use of either method is the following information:

(P/A,6.25%,10)=7.274

Therefore, if a TVM calculator is used, the result of the exact calculation is a factor of 7.274

However, there are two different numbers here. The estimate using linear interpolation is a little bit higher than the exact equation.

Conclusion:

The truth of the matter is that when one is doing an estimate between two time periods and applying the interpolation formula, it is not exact and will have some error. Thus, using the TVM calculator will be the most accurate factor possible.