Question

Jim Ryan, an owner of a Burger King restaurant, assumes that his restaurant will need a new roof in 7 years. He estimates the roof will cost him $9,000 at that time. What amount should Jim invest today at 6% compounded quarterly to be able to pay for the roof

Answer 1

`\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\to &\$9000\\ P=\textit{original amount deposited}\\ r=rate\to 6\%\to (6)/(100)\to &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\to &4\\ t=years\to &7 \end{cases} \\\\\\ 9000=P\left(1+(0.06)/(4)\right)^(4\cdot 7)\implies 9000=P(1.015)^(28)\implies \cfrac{9000}{1.015^(28)}=P`