Problem $1$

Time value You have $$1,500$ to invest today at $8\%$ interest compounded annually.

a$.$ Find how much you will have accumulated in the account after $(1)3$ years, $(2)6$ years, and $(3)10$ years.

b$.$ Use your findings in part a to calculate the amount of interest earned in $(1)$ the first $3$ years $($years $1$ to $3),(2)$ the second $3$ years $($years $4$ to $6),$ and $(3)$ the third $3$ years $($years $7$ to $9).$

c$.$ Compare and contrast your findings in part b$.$ Explain why the amount of interest earned increases in each succeeding $3-$year period.