Question

Ronisha invests $5000 in an account that earns 2.3% annual simple interest. After 3 years, Ronisha invests the interest earned in a second account. This account earns 3.2% annual interest. Ronisha leaves the money in this account until she has earned $55.20 in interest. Ronisha does not deposit or withdraw any money from the accounts. How long does Ronisha invest money into the second account?

Answer 1

Ronisha invests the money into the second account for 5 years.

Explanation:

Answer 2

`~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 2.3\%\to (2.3)/(100)\dotfill &0.023\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (5000)(0.023)(3)\implies I=345`

so then she grabs those 345 earned and puts it in the second account earning 3.2%, how long till that yields 55.20 bucks in interest alone?

`~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$55.20\\ P=\textit{original amount deposited}\dotfill & \$345\\ r=rate\to 3.2\%\to (3.2)/(100)\dotfill &0.032\\ t=years \end{cases} \\\\\\ 55.20 = (345)(0.032)(t)\implies \cfrac{55.20}{(345)(0.032)}=t\implies 5=t`