We can solve this by means of the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where A is the amount of money saved after a time t, r is the rate of interest in decimal, n is the number of times interest is compounded per year and P is the initial amount deposited in the account.
From the statement of the question we know:
P = $100
r = 0.15
n = 4
t = 5 years
we can replace these values into the above formula, to get:
[tex]A=100(1+\frac{0.15}{4})^{4\times5}=208.81[/tex]Then, after 5 years she will have saved $208.81, subtracting the initial amount of money deposited we get the money earned, like this:
money earned = $208.81 - $100 = $108.81
Then, Mandy earns $108.81 after 5 years.
