Question

Hector earned some money doing odd jobs last summer and put it in a savings account that earns 9%interest compounded quarterly after 6 years there is $100.00 in the account how much did Hector earn doing odd jobs

Answer 1

Rate of interest = 9%

Time period =6years

Compound interest is calculated quarterly

After 6 years the amount in the account = $100.00

Expression for compound interest

$\text{ Amount= Principal Amount}(1+\frac{r}{n})^{nt}$

from given data we have,

n=4, t=6, Amount=$100.00

$\begin{gathered} 100=P(1+\frac{0.09}{4})^{4\times6} \\ 100=P(1+\frac{0.09}{4})^{24} \\ 100=P(\frac{4+0.09}{4})^{24} \\ 100=P(\frac{4.09}{4})^{24} \\ 100=P(1.70576) \\ P=\frac{100}{1.70576} \\ P=58.624 \\ \end{gathered}$

So, Principal Amount = $58.624

Answer : Hector earn $58.624