Question

2. Michelle invested $10,000 in an account that earns 8.5% interest that is compounded monthly. Write an exponential model for the balance of the account, then determine the amount of money in the account in 15 years.​

Answer 1

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 10000\\ r=rate\to 8.5\%\to \frac{8.5}{100}\dotfill &0.085\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases}$

$A=10000\left(1+\frac{0.085}{12}\right)^{12\cdot 15}\implies A=10000\left( \frac{2417}{2400} \right)^{180}\implies A\approx 35626.53$