Chapter 5, Problem 1QP

a)

Summary Introduction

To determine: Interest amount earned in the first year.

Explanation of Solution

Given information:

Present value is $1000 and,

Interest rate is 4%

Calculation of amount of interest earned in year 1:

             $\begin{array}{c}\text{Future}\text{value}=\text{Present}\text{value}\times \left(1+\text{r}\right)\\ =\$1,000\times \left(1.04\right)\\ =\$1,040\end{array}$

Hence future value is $1,040

          $\begin{array}{c}\text{Interest}\text{amount}=\text{Future}\text{value}-\text{present}\text{value}\\ =\$1,040-\$1,000\\ =\$40\end{array}$

Hence, the amount interest earned in first year is $40

b)

Summary Introduction

To determine: Interest amount earned in the second year.

Explanation of Solution

Calculation of amount of interest earned in year 2:

              $\begin{array}{c}\text{Future}\text{value}=\text{Present}\text{value}\times {\left(1+\text{r}\right)}^2\\ =\$1,000\times {\left(1.04\right)}^2\\ =\$1,000\times \left(1.0816\right)\\ =\$1,081.60\end{array}$

Hence future value is $1,081.60

           $\begin{array}{c}\text{Interest amount}=\text{Future}\text{value at}\text{year 2}-\text{Future}\text{value at}\text{year 1}\\ =\$1,081.60-\$1,040\\ =\$41.60\end{array}$

Hence, the amount interest earned in second year is $41.60

c)

Summary Introduction

To determine: Interest amount earned in the tenth year.

Explanation of Solution

Calculation of amount of interest earned in year 10:

             $\begin{array}{c}\text{Future}\text{value at year 9}=\text{Present}\text{value}\times {\left(1+\text{r}\right)}^9\\ =\$1,000\times {\left(1.04\right)}^9\\ =\$1,423.31\end{array}$

Hence future value at year 9 is $1,423.31

         $\begin{array}{c}\text{Future}\text{value at year 10}=\text{Present}\text{value}\times {\left(1+\text{r}\right)}^{10}\\ =\$1,000\times {\left(1.04\right)}^{10}\\ =\$1,480.24\end{array}$

Hence future value at year 10 is $1,480.24

         $\begin{array}{c}\text{Interest amount at year 10}=\text{Future}\text{value at}\text{year 10}-\text{Future}\text{value at}\text{year 9}\\ =\$1,480.24-\$1,423.31\\ =\$56.93\end{array}$

Hence, the amount interest earned in tenth year is $56.93