Chapter A, Problem A.1BE

(a)

To determine

Calculate the accumulated amount withdrawn by J, if the investment earns simple interest.

Answer to Problem A.1BE

The accumulated amount withdrawn by J is $9,600.

Explanation of Solution

Future value: This is the amount of present value accumulated or compounded at a rate of interest till a particular future date.

Formula to compute future value at simple interest:

  $\begin{array}{c}\begin{array}{l}\text{Future }\\ \text{value }\end{array}\}\text{= Invested amount + Interest amount}\\ =\text{Present value + }\left(\begin{array}{l}\text{Present value × }\\ \text{Simple interest rate × }\\ \text{Number of years}\end{array}\right)\end{array}$

Determine the accumulated amount withdrawn by J.

  $\begin{array}{c}\begin{array}{l}\text{Future }\\ \text{value }\end{array}\}\text{=Present value + }\left(\begin{array}{l}\text{Present value × }\\ \text{Simple interest rate × }\\ \text{Number of years}\end{array}\right)\\ =\$6,000+\left(\text{\$6,000 × 5\% × 12 years}\right)\\ =\$6,000+\$3,600\\ =\$9,600\end{array}$

The justification for the above calculation is as follows:

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.

Conclusion

Therefore, the accumulated amount withdrawn by J is $9,600.

(b)

To determine

Calculate the future value of a single amount, if the interest is compounded annually.

Answer to Problem A.1BE

Therefore, the future value of an amount is $10.775.16.

Explanation of Solution

Future value: This is the amount of present value accumulated or compounded at a rate of interest till a particular future date.

Formula to compute future value at compounded interest:

  $\text{Future value = Present value}\times {\left(\text{1+Interest rate}\right)}^{\text{Time period}}$

Or,

  $\begin{array}{l}\text{Future}\\ \text{value}\end{array}\}\text{ = }\left\{\begin{array}{l}\text{Invested }\left(\text{present}\right)\text{value × }\\ \text{Future value factor of \$1 at interest rate for time periods}\end{array}\right\}$

Determine the accumulated amount withdrawn by J.

  $\begin{array}{c}\text{Future value}=\left(\begin{array}{l}\text{ Invested amount × }\\ \text{Future value factor of \$1 at 5\% for 12 time periods }\end{array}\right)\\ =\$6,000\times 1.79586\\ =\$10,775.16\end{array}$

Note: Refer to Table 1 of Appendix A for future value factor.

J invested $6,000 at 5% interest rate for 12 years. If the interest amount is compounded annually, the future value factor of 5% for 12 time periods would be 1.79586. Therefore, the amount withdrawn by J is $10.775.16.

Conclusion

Therefore, the future value of an amount is $10.775.16.