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+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$10000\\ r=rate\to 8.5\%\to (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+(0.085)/(12)\right)^(12\cdot 15)\implies A=10000\left( (2417)/(2400) \right)^(180)\implies A\approx 35626.53`