Time value Personal Finance Problem You have $$3,900$ to invest today at $12\%$ interest compounded annually.

a$.$ Find how much you will have accumulated in the account at the end of $(1)4$ years, $(2)8$ years, and $(3)12$ years.

b$.$ Use your findings in part a to calculate the amount of interest earned in $(1)$ the first $4$ years $($years $1$ to $4),(2)$ the second $4$ years $($years $5$ to $8),$ and $(3)$ the third $4$ years $($years $9$ to $12).$

c$.$ Compare and contrast your findings in part b$.$ Explain why the amount of interest earned increases in each succeeding $4-$year period.

a$.(1)$ At the end of $4$ years, the amount you will have accumulated is $$6143\mathrm{.}72.($Round to the nearest cent.$)$