Question

in 3 Years Hannah wants to buy a new bicycle that costs 500.00 if she opens a savings account that earns 15%interest compounded quarterly how much will she have to deposit as principal to have enough money in 3 years to buy the bike

Answer 1

We can solve this problem by means of the formula of the compound interest formula:

$A=P\times(1+\frac{r}{n})^{nt}$

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:

$P=\frac{A}{(1+\frac{r}{n})^{nt}}$

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:

$P=\frac{500}{(1+\frac{0.15}{4})^{4\times3}}=321.45$

Then Hannah, has to deposit $321.45 in order to buy the bicycle in 3 years