Question

Morgan Freeman is investing \(9,069 at the end of each year in a fund that earns 5% interest. In how many years will the fund be at \)100,000?

Short answer

The fund will be at $100,000 in 9 years.

Step-by-step solution

Given information

$\begin{array}{rcl}\mathit{F}\mathit{V}\mathbf{}\mathbf{-}\mathbf{}\mathit{O}\mathit{A}\mathbf{}& \mathbf{=}& \mathbf{}\mathbf{\$}\mathbf{100}\mathbf{,}\mathbf{000}\\ \mathit{R}\mathbf{}& \mathbf{=}& \mathbf{}\mathbf{9069}\\ \mathit{i}\mathbf{}& \mathbf{=}& \mathbf{}\mathbf{5}\mathbf{\%}\end{array}$

Calculation of number of years

$\begin{array}{rcl}\mathit{F}\mathit{V}\mathbf{}\mathbf{-}\mathbf{}\mathit{O}\mathit{A}\mathbf{}& \mathbf{=}& \mathbf{}\mathit{R}\mathbf{(}\mathit{F}\mathit{V}\mathit{F}\mathbf{}\mathbf{-}\mathbf{}\mathit{O}\mathit{A}\mathit{n}\mathbf{,}\mathit{i}\mathbf{)}\\ \mathbf{100}\mathbf{,}\mathbf{000}\mathbf{}& \mathbf{=}& \mathbf{}\mathbf{9069}\mathit{X}\\ \mathit{X}\mathbf{}& \mathbf{=}& \mathbf{}\mathbf{11}\mathbf{.}\mathbf{02657}\\ \mathit{n}\mathbf{}& \mathbf{=}& \mathbf{}\mathbf{9}\mathbf{}\mathit{y}\mathit{e}\mathit{a}\mathit{r}\mathit{s}\end{array}$