Question

Find how much money needs to be deposited now into an account to obtain $1,200 (Future Value) in 15 years if the interest rate is 7% per year compounded monthly (12 times per year).

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 1200\\ P=\textit{original amount deposited}\\ r=rate\to 7\%\to (7)/(100)\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases}`

`1200 = P\left(1+(0.07)/(12)\right)^(12\cdot 15) \implies 1200=P\left( (1207)/(1200) \right)^(180) \\\\\\ \cfrac{1200}{ ~~ \left( (1207)/(1200) \right)^(180) ~~ }=P\implies 421.21\approx P`