Question

You want to have 100,000 fund in 12 years. How much money will you have to deposit now in an account with an APR, annual percentage rate, of 8% and compounding monthly?

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 100000\\ P=\textit{original amount deposited}\\ r=rate\to 8\%\to (8)/(100)\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &12 \end{cases}`

`100000 = P\left(1+(0.08)/(12)\right)^(12\cdot 12)\implies 100000=P\left( (151)/(150) \right)^(144) \\\\\\ \cfrac{100000}{\left( (151)/(150) \right)^(144)}=P\implies \boxed{38411.47\approx P}`