Chapter G, Problem 1BE

(a)

Future Value: The future value is value of present amount compounded at an interest rate until a particular future date. The following formula is used to calculate the future value of an amount:

$\text{Future value of an amount = Present value}\times {\left(\text{1+ Interest rate}\right)}^{\text{Number}\text{of}\text{periods}}$

To determine

The accumulated amount withdrawn by T.

Explanation of Solution

Step 1: Calculate the amount of simple interest.

$\begin{array}{c}\text{Simple interest =}\left(\begin{array}{l}\text{ Principal amount}\times \\ \text{Interest rate}\times \\ \text{Number of periods}\end{array}\right)\\ =\left(\$9,000\times 5\%\times 12\text{ years}\right)\\ =\$5,400\end{array}$

Step 2: Calculate the accumulated amount.

$\begin{array}{c}\text{Accumulated amount = }\left(\begin{array}{l}\text{Invested amount + }\\ \text{Interest amount}\end{array}\right)\\ =\left(\$9,000+\$5,400\right)\\ =\$14,400\end{array}$

Therefore, the accumulated amount withdraw by T is $14,400.

T invested $9,000 at 5% interest rate for 12 years. He withdrew the accumulated amount of money after 12 years. In that, he earned the interest amount of $5,400 from the investment (using simple interest method). Therefore, the accumulated amount withdrawn by T is $14,400.

b)

To determine

To Calculate: The future value of a single amount (if the interest compounded annually).

Explanation of Solution

$\begin{array}{c}\text{Future value of an amount}=\left(\begin{array}{l}\text{ Invested amount × }\\ {\text{Future value of 12}}^{\text{th}}\text{year}\text{at 5\%interest }\\ \left(\text{future value factor}\right)\end{array}\right)\\ =\$9,000\times 1.79586\\ =\$16,162.74\end{array}$

Therefore, the future value of an amount is $16,162.74.

T invested $9,000 at 5% interest rate for 12 years. If the interest amount compounded annually then the future value of a 12^th year at 5% interest would be 1.79586 (Refer table 1 for the future value of money). Therefore, the amount earned by T is $16,162.74.