Question

Sally Medavoy will invest $8,000 a year for 20 years in a fund that will earn 6% annual interest. If the first payment into the fund occurs today, what amount will be in the fund in 20 years? If the first payment occurs at year-end, what amount will be in the fund in 20 years?

Short answer

The amount of funds in 20 years if the first payment occurs today will be $31,1942, and the amount of funds in 20 years if the first payment at the year-end will be $294,285

Step-by-step solution

Calculation of the amount of the fund in 20 years if the first payment occurs today

$\begin{array}{rcl}\mathit{F}\mathit{V}\mathbf{}\mathbf{-}\mathbf{}\mathit{A}\mathit{D}\mathbf{}& \mathbf{=}& \mathbf{}\mathbf{R}\mathbf{(}\mathbf{F}\mathbf{V}\mathbf{F}\mathbf{}\mathbf{-}\mathbf{}\mathbf{A}\mathbf{D}\mathbf{n}\mathbf{,}\mathbf{i}\mathbf{)}\\ & \mathbf{=}& \mathbf{}\mathbf{8}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{38}\mathbf{.}\mathbf{99275}\\ & \mathbf{=}& \mathbf{}\mathbf{\$}\mathbf{311}\mathbf{,}\mathbf{942}\end{array}$

Calculation of the amount of the fund in 20 years if the first payment at the year-end

$\begin{array}{rcl}\mathit{F}\mathit{V}\mathbf{}\mathbf{-}\mathbf{}\mathit{A}\mathit{D}\mathbf{}& \mathbf{=}& \mathbf{}\mathbf{R}\mathbf{(}\mathbf{F}\mathbf{V}\mathbf{F}\mathbf{}\mathbf{-}\mathbf{}\mathbf{O}\mathbf{A}\mathbf{n}\mathbf{,}\mathbf{i}\mathbf{)}\\ & \mathbf{=}& \mathbf{}\mathbf{8}\mathbf{,}\mathbf{000}\mathbf{}\mathbf{\times }\mathbf{}\mathbf{36}\mathbf{.}\mathbf{7855}\\ & \mathbf{=}& \mathbf{}\mathbf{\$}\mathbf{}\mathbf{294}\mathbf{,}\mathbf{285}\end{array}$