Question

Airen’s grandparents deposited $1300 in a mutual fund earning 6% interest compounded annually. Write an equation to represent how much money (y) Airen would have after x years. Use your equation to determine how much money Airen would have in the account after 18 years.

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount \underline{in 18 years}} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1300\\ r=rate\to 6\%\to (6)/(100)\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &18 \end{cases}`

`A=1300\left(1+(0.06)/(1)\right)^(1\cdot 18)\implies A=1300(1.06)^(18)\implies A\approx 3710.64 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y = 1300(1.06)^x~\hfill`