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.

Respuesta :

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill&\$148700\\ P=\textit{original amount deposited}\\ r=rate\to 3.51\%\to \frac{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}[/tex]

[tex]148700=P\left(1+\frac{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}[/tex]