Question

What amount should you invest now if after 4 years you want a final value of $15000 based on 6%

interest compounded quarterly?

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\$15000\\ P=\textit{original amount deposited}\\ r=rate\to 6\%\to (6)/(100)\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}`

`15000=P\left(1+(0.06)/(4)\right)^(4\cdot 4)\implies 15000=P(1.015)^(16) \\\\\\ \cfrac{15000}{1.015^(16)}=P\implies 11820.47\approx P`