Since the interest rate is 13% compounded quarterly, then an increase of 13÷4 percent is applied each 3 months. In 6 years, there are 24 of such periods.
Let I be the initial amount of money.
Each three monts, the balance gets multiplied by a factor of:
[tex]1+\frac{13\div4}{100}=1.0325[/tex]Therefore, after 6 years, the balance will be:
[tex]I\cdot(1.0325)^{24}[/tex]Since after that time, the balance is $700.00, then:
[tex]\begin{gathered} I\cdot(1.0325)^{24}=700 \\ \Rightarrow I=\frac{700}{1.0325^{24}} \\ =\frac{700}{2.154574\ldots} \\ =324.89 \end{gathered}[/tex]Therefore, Shannon earned $324.89 doing odd jobs.
