Question

Tony Bautista needs $25,000 in 4 years. What amount must he invest today if his investment earns 12% compounded annually? What amount must he invest if his investment earns 12% annual interest compounded quarterly?

Short answer

The amount he must invest when he earns 12% compounded annually is $15,888, and the amount he must invest when he earns 12% compounded quarterly is $15,579.

Step-by-step solution

Calculation of amount he must invest when he earns 12% compounded annually

$\begin{array}{rcl}\mathit{P}\mathit{V}& \mathbf{=}& \mathit{F}\mathit{V}\mathbf{(}\mathit{P}\mathit{V}\mathit{F}\mathit{n}\mathbf{,}\mathit{i}\mathbf{)}\\ & \mathbf{=}& \mathbf{25}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{63552}\\ & \mathbf{=}& \mathbf{\$}\mathbf{15}\mathbf{,}\mathbf{888}\end{array}$

Calculation of amount he must invest when he earns 12% compounded quarterly

$\begin{array}{rcl}\mathit{P}\mathit{V}& \mathbf{=}& \mathit{F}\mathit{V}\mathbf{(}\mathit{P}\mathit{V}\mathit{F}\mathit{n}\mathbf{,}\mathit{i}\mathbf{)}\\ & \mathbf{=}& \mathbf{25}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{62317}\\ & \mathbf{=}& \mathbf{15}\mathbf{,}\mathbf{579}\end{array}$