Question

Brian needs $50,000 for a down payment on a home in 5 years.  How much must he deposit into an account that pays 1.16% interest compounded quarterly, in order to meet his goal?

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$50000\\ P=\textit{original amount deposited}\dotfill &\$P\\ r=rate\to 1.16\%\to (1.16)/(100)\dotfill &0.0116\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &5 \end{cases}`

`50000=P\left(1+(0.0116)/(4)\right)^(4\cdot 5) \implies 50000=P(1.0029)^(20) \\\\\\ \cfrac{50000}{(1.0029)^(20)}=P\implies {\Large \begin{array}{llll} 47186.46\approx P \end{array}}`