Chapter AG, Problem G.1BE

To determine

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 amounts withdraw by J.

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

Explanation of Solution

Step 1: Calculate the amount of simple interest.

$\begin{array}{c}\text{Simple interest =}\left(\begin{array}{l}\text{ Principal amount}\times \\ \text{Interest rate}\times \\ \text{Number of periods}\end{array}\right)\\ =\left(\$6,000\times 5\%\times 12\text{ years}\right)\\ =\$3,600\end{array}$

Step 2: Calculate the accumulated amount.

$\begin{array}{c}\text{Accumulated amount = }\left(\begin{array}{l}\text{Invested amount + }\\ \text{Interest amount}\end{array}\right)\\ =\left(\$6,000+\$3,600\right)\\ =\$9,600\end{array}$

Therefore, the accumulated amount withdraw by J is $9,600.

J invested $6,000 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 $3,600 from the investment (using simple interest method). Therefore, the accumulated amount withdraw by J is $9,600.

The future value of the amount is determined as follows:

$\begin{array}{c}\text{Future value of an amount}=\left(\begin{array}{l}\text{ Invested amount × }\\ {\text{Future value of 12}}^{\text{th}}\text{year}\text{at 5\%interest }\\ \left(\text{future value factor}\right)\end{array}\right)\\ =\$6,000\times 1.79586\\ =\$10,775.16\end{array}$

J invested $6,000 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 earn by J is $10.775.16. Therefore, the future value of an amount is $10.775.16.