Question

If Jesus invests $600 per month for 30 years and it earns 8% annual interest compounded monthly, how much will the future value of his investment be worth?

Answer 1

`\bf \qquad \qquad \textit{Future Value of an ordinary annuity} \\\\ A=pymnt\left[ \cfrac{\left( 1+(r)/(n) \right)^(nt)-1}{(r)/(n)} \right] \\\\\\ \qquad \begin{cases} A= \begin{array}{llll} \textit{accumulated amount}\\ \end{array}\\ pymnt=\textit{periodic payments}\to &600\\ r=rate\to 8\%\to (8)/(100)\to &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus} \end{array}\to &12\\ t=years\to &30 \end{cases}`


`\bf A=600\left[ \cfrac{\left( 1+(0.08)/(12) \right)^(12\cdot 30)-1}{(0.08)/(12)} \right]`

I'm thinking he may make more money turning water into booze though, for 30years, I could be mistaken, who knows