Question

A newborn child receives a ​$9,000 gift toward a college education from her grandparents. How much will the ​$9,000 be worth in 18 years if it is invested at 7.6% compounded​ quarterly? Round to the nearest cent.

Answer 1

`\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$9000\\ r=rate\to 7.6\%\to (7.6)/(100)\to &0.076\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\to &4\\ t=years\to &18 \end{cases} \\\\\\ A=9000\left(1+(0.076)/(4)\right)^(4\cdot 18)\implies A=9000(1.019)^(72)`