We can solve this problem by means of the formula of the compound interest formula:
[tex]A=P\times(1+\frac{r}{n})^{nt}[/tex]Where A is the amount of money saved in the account after a time t, P is the principal, r is the rate of interest in decimals and n is the number of times interest is compound per year.
If we solve for P from this equation, we get:
[tex]P=\frac{A}{(1+\frac{r}{n})^{nt}}[/tex]From the statement of the question we know that:
A = $500, since this is the amount of money that Hannah wants to save
n = 4
t = 3 years
r = 15/100 = 0.15
If we replace these values into the equation above, we get:
[tex]P=\frac{500}{(1+\frac{0.15}{4})^{4\times3}}=321.45[/tex]Then Hannah, has to deposit $321.45 in order to buy the bicycle in 3 years
