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+(r)/(n))^(nt)`

from given data we have,

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

`\begin{gathered} 100=P(1+(0.09)/(4))^(4*6) \\ 100=P(1+(0.09)/(4))^(24) \\ 100=P((4+0.09)/(4))^(24) \\ 100=P((4.09)/(4))^(24) \\ 100=P(1.70576) \\ P=(100)/(1.70576) \\ P=58.624 \\ \end{gathered}`

So, Principal Amount = $58.624

Answer : Hector earn $58.624