A principal of $3200 is invested at 7.75% interest, compounded annually. How much will the investment be worth after 13 years?

1 answer:

6 0

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3200\\ r=rate\to 7.75\%\to \frac{7.75}{100}\dotfill &0.0775\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &13 \end{cases} \\\\\\ A=3200\left(1+\frac{0.0775}{1}\right)^{1\cdot 13}\implies A=3200(1.0775)^{13}\implies A\approx 8444.51$

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