Question

Alan Jackson invests $20,000 at 8% annual interest, leaving the money invested without withdrawing any of the interest for 8 years. At the end of the 8 years, Alan withdraws the accumulated amount of money. Instructions (a) Compute the amount Alan would withdraw assuming the investment earns simple interest. (b) Compute the amount Alan would withdraw assuming the investment earns interest compounded annually. (c) Compute the amount Alan would withdraw assuming the investment earns interest compounded semiannually

Short answer

The amount at the withdrawal using simple interest will be $32,800, Compounded annually will be $37,018, and compounded semi-annually will be $37,459.

Step-by-step solution

Simple Interest

$$\begin{gathered} \mathbf{Amount}\mathbf{}\mathbf{at}\mathbf{}\mathbf{withdrawal}\mathbf{=}\mathbf{Amount}\mathbf{+}\mathbf{Simple}\mathbf{}\mathbf{Interest}\mathbf{}\mathbf{Rate} \\ \mathbf{=}\mathbf{20}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{20}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{8}\mathbf{\%}\mathbf{\times }\mathbf{8} \\ \mathbf{=}\mathbf{\$}\mathbf{32}\mathbf{,}\mathbf{800} \end{gathered}$$

Compounded Annually

$$\begin{gathered} \mathbf{Amount}\mathbf{}\mathbf{at}\mathbf{}\mathbf{withdrawal}\mathbf{=}\mathbf{Amount}\mathbf{\times }\mathbf{Future}\mathbf{}\mathbf{value}\mathbf{}\mathbf{factor} \\ \mathbf{=}\mathbf{20}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{1}\mathbf{.}\mathbf{85093} \\ \mathbf{=}\mathbf{\$}\mathbf{37}\mathbf{,}\mathbf{018} \end{gathered}$$

Compounded Semi-annually

$$\begin{gathered} \mathbf{Amount}\mathbf{}\mathbf{at}\mathbf{}\mathbf{withdrawal}\mathbf{=}\mathbf{Amount}\mathbf{\times }\mathbf{Future}\mathbf{}\mathbf{value}\mathbf{}\mathbf{factor} \\ \mathbf{=}\mathbf{20}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{1}\mathbf{.}\mathbf{87298} \\ \mathbf{=}\mathbf{\$}\mathbf{37}\mathbf{,}\mathbf{459} \end{gathered}$$