Question

Erin wants to invest $3,600.00 in a savings account that pays 4.42% simple interest. How long will it take for this investment to reach a value of $6,700.00?

Round your answer to the nearest tenth of a year.

It will take
years for the investment to reach a value of $6,700.00.

Answer 1

`~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6700\\ P=\textit{original amount deposited}\dotfill & \$3600\\ r=rate\to 4.42\%\to (4.42)/(100)\dotfill &0.0442\\ t=years \end{cases} \\\\\\ 6700=3600[1+(0.0442)(t)]\implies \cfrac{6700}{3600}=1+0.0442t\implies \cfrac{67}{36}=1+0.0442t \\\\\\ \cfrac{67}{36}-1=0.0442t\implies \cfrac{31}{36}=0.0442t\implies \cfrac{(31)/(36)}{0.0442}=t\implies 19.5\approx t`