Question

Eric is opening a savings account that earns 3.5% interest compounded semiannually. How much will be in the account after 5 years if his initial investment is $15,000?

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 &\$15000\\ r=rate\to 3.5\%\to (3.5)/(100)\dotfill &0.035\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &5 \end{cases}`

`A=15000\left(1+(0.035)/(2)\right)^(2\cdot 5)\implies A=15000(1.0175)^(10) \implies A \approx 17841.67`