Question

Anthony is going to invest in an account paying an interest rate of 4. 6% compounded

monthly. How much would Anthony need to invest, to the nearest ten dollars, for the


value of the account to reach $240,000 in 20 years?

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 240000\\ P=\textit{original amount deposited}\\ r=rate\to 4.6\%\to (4.6)/(100)\dotfill &0.046\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases}`

`240000 = P\left(1+(0.046)/(12)\right)^(12\cdot 20) \implies 240000=P\left( \cfrac{6023}{6000} \right)^(240) \\\\\\ \cfrac{240000}{ ~~ \left( (6023)/(6000) \right)^(240) ~~ }=P\implies 95810\approx P`