Question

Your bank pays 6.50 percent annual interest compounded semiannually on your savings account. you don’t expect to add to the current balance of $2,000 over the next four years. how much money can you expect to have at the end of this period?

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 &\$2000\\ r=rate\to 6.50\%\to (6.50)/(100)\dotfill &0.065\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &4 \end{cases} \\\\\\ A=2000\left(1+(0.065)/(2)\right)^(2\cdot 4)\implies A=2000(1.0325)^8\implies A\approx 2583.16`