Calculate the future value of $$6,000$ in

a$.4$ years at an interest rate of $9\%$ per year.

b$.8$ years at an interest rate of $9\%$ per year.

c$.4$ years at an interest rate of $18\%$ per year.

d$.$ Why is the amount of interest earned in part $($a$)$ less than half the amount of interest earned in part $($b$)?$

a$.$ Calculate the future value of $$6,000$ in $4$ years at an interest rate of $9\%$ per year.

The future value of $$6,000$ in $4$ years at an interest rate of $9\%$ per year is $ $($Round to the nearest cent.$)$

b$.$ Calculate the future value of $$6,000$ in $8$ years at an interest rate of $9\%$ per year.

The future value of $$6,000$ in $8$ years at an interest rate of $9\%$ per year is : $($Round to the nearest cent.$)$

c$.$ Calculate the future value of $$6,000$ in $4$ years at an interest rate of $18\%$ per year.

The future value of $$6,000$ in $4$ years at an interest rate of $18\%$ per year is $ $($Round to the nearest cent.$)$

d$.$ Why is the amount of interest earned in part $($a$)$ less than half the amount of interest earned in part $($b$)?($Select the best choice below.$)$

A$.$ This results because you earn more interest on past interest. As interest is earned on the increasing amount of accumulated interest, the money grows faster as time goes on$.$

B$.$ The amount of interest earned in part $($a$)$ is really half of the amount of interest earned in part $($b$)$ since in part $($b$)$ the money grows for twice as many years as in part $($a$).$

C$.$ The annual interest rate in part $($b$)$ is slightly higher than the rate assumed in part $($a$).$ This is because of compounding.

D$.$ The interest earned in part $($a$)$ is based on a lower effective annual interest rate.