Chapter 5, Problem 4QP

Calculating Interest Kates [LO3] Solve for the unknown interest rate in each of the following:

Summary Introduction

To calculate: The rate of return

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

Answer to Problem 4QP

The rate of return is as follows:

Particulars	Present value	Years	Interest Rate	Future value
Investment A	$181	4	13.18%	$297
Investment B	$335	18	6.72%	$1,080
Investment C	$48,000	19	7.37%	$185,382
Investment D	$40,353	25	10.86%	$531,618

Explanation of Solution

Given information:

Investment A has a present value of $181, future value of $297, and a 4-year investment period. Investment B has a present value of $335, future value of $1,080, and an 18-year investment period.

Investment C has a present value of $48,000, future value of $185,382, and a 19-year investment period. Investment D has a present value of $40,353, future value of $531,618, and a 25-year investment period.

The formula to calculate the rate of return:

$\text{P}\times {\left(1+r\right)}^t=\text{FV}$

Where,

“P” refers to the principal amount invested

“r” refers to the rate of interest or return

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return of Investment A:

$\begin{array}{c}\text{P}\times {\left(1+r\right)}^t=\text{FV}\\ \$181\times {\left(1+r\right)}^4=\$297\\ {\left(1+r\right)}^4=\frac{\$297}{\$181}\\ {\left(1+r\right)}^4=1.6409\end{array}$

$\begin{array}{c}1+r={1.6409}^{\frac{1}{4}}\\ r=1.1318-1\\ r=0.1318\text{ or }13.18\%\end{array}$

Hence, the rate of return of Investment A is 13.18%.

Compute the rate of return of Investment B:

$\begin{array}{c}\text{P}\times {\left(1+r\right)}^t=\text{FV}\\ \$335\times {\left(1+r\right)}^{18}=\$1,080\\ {\left(1+r\right)}^{18}=\frac{\$1,080}{\$335}\\ {\left(1+r\right)}^{18}=3.2239\end{array}$

$\begin{array}{c}1+r={3.2239}^{\frac{1}{18}}\\ r=1.0672-1\\ r=0.0672\text{ or }6.72\%\end{array}$

Hence, the rate of return Investment B is 6.72%.

Compute the rate of return of Investment C:

$\begin{array}{c}\text{P}\times {\left(1+r\right)}^t=\text{FV}\\ \$48,000\times {\left(1+r\right)}^{19}=\$185,382\\ {\left(1+r\right)}^{19}=\frac{\$185,382}{\$48,000}\\ {\left(1+r\right)}^{19}=3.8621\end{array}$

$\begin{array}{c}1+r={3.8621}^{\frac{1}{19}}\\ r=1.0737-1\\ r=0.0737\text{ or }7.37\%\end{array}$

Hence, the rate of return Investment C is 7.37%.

Compute the rate of return of Investment D:

$\begin{array}{c}\text{P}\times {\left(1+r\right)}^t=\text{FV}\\ \$40,353\times {\left(1+r\right)}^{25}=\$531,618\\ {\left(1+r\right)}^{25}=\frac{\$531,618}{\$40,353}\\ {\left(1+r\right)}^{25}=13.1742\end{array}$

$\begin{array}{c}1+r={13.1742}^{\frac{1}{25}}\\ r=1.1086-1\\ r=0.1086\text{ or }10.86\%\end{array}$

Hence, the rate of return Investment D is 10.86%.