Time value Personal Finance Problem You have $$1,400$ to invest today at $9\%$ interest compounded annually.

a$.$ Find how much you will have accumulated in the account at the end of $(1)5$ years, $(2)10$ years, and $(3)15$ years.

b$.$ Use your findings in part a to calculate the amount of interest earned in $(1)$ the first $5$ years $($years $1$ to $5),(2)$ the second $5$ years $($years $6$ to $10),$ and $(3)$ the third $5$ years $($years $11$ to $15).$

c$.$ Compare and contrast your findings in part b$.$ Explain why the amount of interest earned increases in each succeeding $5-$year period.

a$.(1)$ At the end of $5$ years, the amount you will have accumulated is $

$($Round to the nearest cent.$)$

$(2)$ At the end of $10$ years, the amount you will have accumulated is $

$($Round to the nearest cent.$)$

$(3)$ At the end of $15$ years, the amount you will have accumulated is $

$($Round to the nearest cent.$)$

b$.(1)$ From your findings in part a$,$ the amount of interest earned in the first $5$ years $($years $1$ to $5)$ is $

$($Round to the nearest cent.$)$

$(2)$ From your findings in part a$,$ the amount of interest earned in the second $5$ years $($years $6$ to $10)$ is $

$($Round to the nearest cent.$)$

$(3)$ From your findings in part a$,$ the amount of interest earned in the third $5$ years $($years $11$ to $15)$ is $

$($Round to the nearest cent.$)$

c$.$ According to the findings in part $b,$ the amount of interest earned

in each succeeding $5-$year period due to

$,$ the earning of interest on previous interest earned.

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