Question

Shannon earned some money doing odd jobs last summer and put it in a savings account that earns 13%interest compounded quarterly. after 6 years there is $700.00 in the account how much did Shannon earn doing odd jobs

Answer 1

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:

`1+(13/4)/(100)=1.0325`

Therefore, after 6 years, the balance will be:

`I\cdot(1.0325)^(24)`

Since after that time, the balance is $700.00, then:

`\begin{gathered} I\cdot(1.0325)^(24)=700 \\ \Rightarrow I=(700)/(1.0325^(24)) \\ =(700)/(2.154574\ldots) \\ =324.89 \end{gathered}`

Therefore, Shannon earned $324.89 doing odd jobs.