Question

On Melissa's 6th birthday, she gets a $6000 CD that earns 7% interest, compounded semiannually. If the CD matures on her 14th birthday, how much money will be available?

Answer 1

if the CD matures on her 14th birthday, that means 8 years after she got it, since she got it in her 6th birthday, so

`~~~~~~ \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 &\$6000\\ r=rate\to 7\%\to (7)/(100)\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &8 \end{cases} \\\\\\ A=6000\left(1+(0.07)/(2)\right)^(2\cdot 8)\implies A=6000(1.035)^(16)\implies A\approx 10403.92`