Question

Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What interest rate did she earn? Use the formula I=Prt to find your answer, where l is interest, P is principal, r is rate and t is time. Enter your solution in decimal form rounded to the nearest hundredth. For example, if you solution is 20% you would enter 0.12.

Answer 1

$\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill&\ 450\\ P=\textit{original amount deposited}\dotfill & \ 3000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &3 \end{cases} \\\\\\ 450=3000\left( \frac{r}{100} \right)(3)\implies 450=\cfrac{3000\cdot 3}{100}r \\\\\\ 450=90r\implies \cfrac{450}{90}=r\implies 5=r\implies \stackrel{\textit{in decimal}}{0.05=r}$