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Part $1$

Calculate the future value of $$$$10$ comma $000$ in

a$.5$ years at an interest rate of $10\%$ per year.

b$.10$ years at an interest rate of $10\%$ per year.

c$.5$ years at an interest rate of $20\%$ per year.

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

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Part $1$

a$.$ Calculate the future value of $$$$10$ comma $000$ in $5$ years at an interest rate of $10\%$ per year.

The future value of $$$$10$ comma $000$ in $5$ years at an interest rate of $10\%$ per year is $$$

$$

enter your response here. $($Round to the nearest$$ cent.$)$

Part $2$

b$.$ Calculate the future value of $$$$10$ comma $000$ in $10$ years at an interest rate of $10\%$ per year.

The future value of $$$$10$ comma $000$ in $10$ years at an interest rate of $10\%$ per year is $$$

$$

enter your response here. $($Round to the nearest$$ cent.$)$

Part $3$

c$.$ Calculate the future value of $$$$10$ comma $000$ in $5$ years at an interest rate of $20\%$ per year.

The future value of $$$$10$ comma $000$ in $5$ years at an interest rate of $20\%$ per year is $$$

$$

enter your response here. $($Round to the nearest$$ cent.$)$

Part $4$

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$.$

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

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

D$.$

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$.$