Question

James took out a loan at a rate of 8,5% for 6 months. He had to payback $1876.50. How much did he borrow?

Answer 1

now, assuming is simple interest applied.

bearing in mind that 6 months is not even a year, is really 6/12 of a year.

$\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&1876.50\\ P=\textit{original amount deposited}\\ r=rate\to 8.5\%\to \frac{8.5}{100}\dotfill &0.085\\ t=years\to \frac{6}{12}\dotfill &\frac{1}{2} \end{cases} \\\\\\ 1876.50=P\left[ 1+(0.085)\left( \frac{1}{2} \right) \right]\implies 1876.5=P(1.0425) \\\\\\ \cfrac{1876.5}{1.0425}=P\implies 1800=P$