Question

Skylar is going to invest in an account paying an interest rate of 6. 4% compounded monthly. How much would Skylar need to invest, to the nearest ten dollars, for the value of the account to reach $300 in 17 years?

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 300\\ P=\textit{original amount deposited}\\ r=rate\to 6.4\%\to (6.4)/(100)\dotfill &0.064\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &17 \end{cases}`

`300 = P\left(1+(0.064)/(12)\right)^(12\cdot 17) \implies 300=P\left( (377)/(375) \right)^(204) \implies \cfrac{300}{ ~~ \left( (377)/(375) \right)^(204) ~~ }=P \\\\\\ \cfrac{300}{ ~~ (377^(204))/(375^(204)) ~~ }=P\implies 300\cdot \cfrac{375^(204)}{377^(204)}=P\implies 100\approx P`