Question

an amount of 44000 is borrowed for 14 years at 7.5 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

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 44000\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &14 \end{cases}$

$\bf A=44000\left(1+\frac{0.075}{1}\right)^{1\cdot 14}\implies A=44000(1.075)^{14} \\\\\\ A\approx 121107.538\implies \stackrel{\textit{rounded up}}{A=121108}$