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 7.1% compounded​ quarterly? Round to the nearest cent.

Answer 1

`\bf \qquad \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 7.1\%\to (7.1)/(100)\to &0.071\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, means} \end{array}\to &4\\ t=years\to &18 \end{cases} \\\\\\ A=9000\left(1+(0.071)/(4)\right)^(4\cdot 18)`

Answer 2

amount after 18 years = 9000(1 + (0.071/ 4) ^ (4*18)

= $ 31,944.97