Question

Henry Quincy wants to withdraw $30,000 each year for 10 years from a fund that earns 8% interest. How much must he invest today if the first withdrawal is at year-end? How much must he invest today if the first withdrawal takes place immediately?

Short answer

The amount he should invest today if the first withdrawal is at the end of the year will be $201,302, and the amount will be $217,407 when the withdrawal takes place immediately.

Step-by-step solution

Calculation of the amount to be invested if first withdrawal is at year-end

$\begin{array}{rcl}\mathit{P}\mathit{V}\mathbf{}\mathbf{-}\mathbf{}\mathit{O}\mathit{A}\mathbf{}& \mathbf{=}& \mathbf{}\mathit{R}\mathbf{(}\mathit{P}\mathit{V}\mathit{F}\mathbf{}\mathbf{-}\mathbf{}\mathit{O}\mathit{A}\mathit{n}\mathbf{,}\mathit{i}\mathbf{)}\\ & \mathbf{=}& \mathbf{}\mathbf{30}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{}\mathbf{6}\mathbf{.}\mathbf{71008}\\ & \mathbf{=}& \mathbf{}\mathbf{\$}\mathbf{201}\mathbf{,}\mathbf{302}\end{array}$

Calculation of the amount to be invested if the first withdrawal takes place immediately

$\begin{array}{rcl}\mathit{P}\mathit{V}\mathbf{}\mathbf{-}\mathbf{}\mathit{A}\mathit{D}\mathbf{}& \mathbf{=}& \mathbf{}\mathit{R}\mathbf{(}\mathit{P}\mathit{V}\mathit{F}\mathbf{}\mathbf{-}\mathbf{}\mathit{A}\mathit{D}\mathbf{)}\mathbf{}\\ & \mathbf{=}& \mathbf{}\mathbf{30}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{7}\mathbf{.}\mathbf{24689}\\ \mathbf{}& \mathbf{=}& \mathbf{}\mathbf{\$}\mathbf{217}\mathbf{,}\mathbf{407}\end{array}$