Chapter 5, Problem 92RE

(a)

To determine

To find: The annual rate of interest offered.

Answer to Problem 92RE

The annual rate of interest offeredis $10.45\%$ .

Explanation of Solution

Given information:

The initial deposit amount and the time required for the matured amount of $\$5000$ is given.

The annual rate of interest offeredis calculated as,

  $\begin{array}{l}A=P{e}^{rt}\\ 5000=620.17e^{r\times 20}\\ 8.062=e^{20r}\\ r=0.1045\times 100\%\end{array}$

Simplify further,

  $r=10.45\%$

Thus, the annual rate of interest offeredis $10.45\%$ .

(b)

To determine

To find: The actual value of the amount in $20\text{years}$ .

Answer to Problem 92RE

The actual value of the amount in $20\text{years}$ is $\$32250.14$ .

Explanation of Solution

Given information:

The initial deposit amount is $\$4000$ and the time required for the matured is $20\text{years}$ .

The actual value of the amount in $20\text{years}$ is calculated as,

  $\begin{array}{c}A=P{e}^{rt}\\ =\left(4000\right)e^{0.1045\times 20}\\ =\$32250.14\end{array}$

Thus, the actual value of the amount in $20\text{years}$ is $\$32250.14$ .