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likoan [24]
2 years ago
13

On Melissa's 6th birthday, she gets a $6000 CD that earns 7% interest, compounded semiannually. If the CD matures on her 14th bi

rthday, how much money will be available?
Mathematics
1 answer:
pashok25 [27]2 years ago
7 0

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+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6000\\ r=rate\to 7\%\to \frac{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+\frac{0.07}{2}\right)^{2\cdot 8}\implies A=6000(1.035)^{16}\implies A\approx 10403.92

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