Question

Question:The Kellys are planning for a retirement home. They estimate they will need $200,000 4 years from now to purchase this home. Assuming an interest rate of 10%, what amount must be deposited at the end of each of the 4 years to fund the home price? (Round to two decimal places.)

Short answer

The amount to be deposited each year will be $43094

Step-by-step solution

Step-by-stem solutionStep 1

Future values of annuity refer to the total value of a series of recurring payments at some specific date in the future.

Step 2

$$\begin{gathered} \mathbf{Amount}\mathbf{}\mathbf{}\mathbf{deposited}\mathbf{}\mathbf{}\mathbf{each}\mathbf{}\mathbf{year}\mathbf{=}\frac{\mathbf{Amount}\mathbf{}\mathbf{needed}}{\mathbf{Rate}\mathbf{(}\mathbf{future}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{}\mathbf{an}\mathbf{}\mathbf{}\mathbf{ordinary}\mathbf{}\mathbf{}\mathbf{annuity}\mathbf{}\mathbf{at}\mathbf{}\mathbf{10}\mathbf{\%}\mathbf{}\mathbf{for}\mathbf{}\mathbf{4}\mathbf{}\mathbf{years}\mathbf{)}} \\ \mathbf{=}\frac{\mathbf{200000}}{\mathbf{4}\mathbf{.}\mathbf{64100}} \\ \mathbf{=}\mathbf{\$}\mathbf{43094} \end{gathered}$$