Question

Rachel invests $6,500 into a 5-year CD. The interest rate is 4.2% and is compounded semi-annually. How much will she have in her account at the end of the 5 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 &\$6500\\ r=rate\to 4.2\%\to (4.2)/(100)\dotfill &0.042\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &5 \end{cases} \\\\\\ A=6500\left(1+(0.042)/(2)\right)^(2\cdot 5)\implies A=6500(1.021)^(10)\implies A\approx 8001.49`