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11111nata11111 [884]
2 years ago
14

Jim Ryan, an owner of a Burger King restaurant, assumes that his restaurant will need a new roof in 7 years. He estimates the ro

of 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
Mathematics
1 answer:
Lelu [443]2 years ago
6 0
\bf ~~~~~~ \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\to &\$9000\\
P=\textit{original amount deposited}\\
r=rate\to 6\%\to \frac{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+\frac{0.06}{4}\right)^{4\cdot 7}\implies 9000=P(1.015)^{28}\implies \cfrac{9000}{1.015^{28}}=P
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