Question

How much would you have to deposit in an account with a 7% interest rate, compounded monthly, to have $1100 in

your account 10 years later?
P = $[?]
Round to the nearest cent.

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 1100\\ 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 &10 \end{cases}`

`1100 = P\left(1+(0.07)/(12)\right)^(12\cdot 10) \implies 1100=P\left(1+(7)/(1200)\right)^(120) \\\\\\ 1100=P\left((1207)/(1200)\right)^(120)\implies \cfrac{1100}{ ~~ \left((1207)/(1200)\right)^(120) ~~ }=P\implies 537.36\approx P`