Question

At the end of year 5, the account was valued at $3203.19. At the end of year 6, the account was valued at $3315.30. What was the interest rate, as a percent?

Answer 1

well, from the end of year 5 to the end of year 6 is only 1 year later, so

`~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$3315.30\\ P=\textit{original amount deposited}\dotfill & \$3203.19\\ r=rate\to r\%\to (r)/(100)\\ t=years\dotfill &1 \end{cases} \\\\\\ 3315.30=3203.19[1+((r)/(100))(1)] \implies \cfrac{3315.30}{3203.19}=1+\cfrac{r}{100} \\\\\\ \cfrac{3315.30}{3203.19}-1=\cfrac{r}{100}\implies 100\left( \cfrac{3315.30}{3203.19}-1 \right)=r\implies \stackrel{\%}{3.5}\approx r`