Question

To help with his retirement savings, Shen has decided to invest.

Assuming an interest rate of 3.51% compounded monthly, how much would he have to invest to
have $148,700 after 18 years?

Do not round any intermediate computations, and round your final answer to the nearest dollar.

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill&\$148700\\ P=\textit{original amount deposited}\\ r=rate\to 3.51\%\to (3.51)/(100)\dotfill &0.0351\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &18 \end{cases}`

`148700=P\left(1+(0.0351)/(12)\right)^(12\cdot 18)\implies 148700=P(1.002925)^(216) \\\\\\ \cfrac{148700}{(1.002925)^(216)}=P\implies 79126.913\approx P\implies \stackrel{\textit{rounded up}}{79127\approx P}`