Question

3 years ago Clara won some money in the lottery and put it in a savings account that earns 8%interest compounded quarterly if Clara currently has 700.00 in the bank account how much interest has she earned

Answer 1

In order to calculate Clara's interest after 3 years, we can use the following formula for compound interest:

$P=P_0\cdot(1+\frac{i}{n})^{nt}$

Where P is the final amount after t years, P0 is the initial value, i is the rate of interest and n is a factor that depends on the compound rate (for quarterly we use n = 4)

So using P = 700, i = 8% = 0.08, t = 3 and n = 4, we have:

$\begin{gathered} 700=P_0\cdot(1+\frac{0.08}{4})^{3\cdot4} \\ 700=P_0\cdot(1+0.02)^{12} \\ 700=P_{0\cdot}1.2682418 \\ P_0=\frac{700}{1.2682418}=551.94 \end{gathered}$

If the initial amount of money Clara put is 551.94, the total interest she earned is the difference between the final and the initial value:

$700-551.94=148.06$

So Clara earned $148.06.