Question

An amount of $38,000 is borrowed for 6 years at 4.75% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?

Round your answer to the nearest dollar.

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 &\$38000\\ r=rate\to 4.75\%\to (4.75)/(100)\dotfill &0.0475\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &6 \end{cases} \\\\\\ A = 38000\left(1+(0.0475)/(1)\right)^(1\cdot 6)\implies A=38000(1.0475)^6 \implies A \approx 50200`