Question

To have $6,000 for a child’s education in 10 years, what amount should a parent deposit in a savings account that earns 12% 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 & \$ 6000\\ P=\textit{original amount deposited}\\ r=rate\to 12\%\to (12)/(100)\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &10 \end{cases}`

`6000 = P\left(1+(0.12)/(4)\right)^(4\cdot 10) \implies 6000=P1.03^(40) \\\\\\ \cfrac{6000}{1.03^(40)}=P\implies 1839.34\approx P`