Question

An amount of $37,000 is borrowed for 6 years at 8.25% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be
paid back?
Use the calculator provided and round your answer to the nearest dollar
?

Answer 1

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 37000\\ r=rate\to 8.25\%\to \frac{8.25}{100}\dotfill &0.0825\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &6 \end{cases}$

$\bf A=37000\left(1+\frac{0.0825}{1}\right)^{1\cdot 6}\implies A=37000(1.0825)^6 \\\\\\ A \approx 59534.561\implies \stackrel{\textit{rounded up}}{A=59535}$