Question

Miguel invests money in an account paying simple interest. He invests $170 and no money is added or removed from the investment. After one year, he has $185.30. What is the simple percent interest per year?

Answer 1

$~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \ 185.30\\ P=\textit{original amount deposited}\dotfill & \ 170\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &1 \end{cases} \\\\\\ 185.30=170[1+(\frac{r}{100})(1)]\implies \cfrac{185.30}{170}=1+\cfrac{r}{100}\implies \cfrac{109}{100}=\cfrac{100+r}{100} \\\\\\ 109=100+r\implies \stackrel{\%}{9}=r$