Calculating compound interest with non$-$annual periods$)($Related to Checkpoint $5\mathrm{.}2$ on page $168)$ You just received a $$5,000$ bonus.

a$.$ Calculate the future value of $$5,000,$ given that it will be held in the bank for five years and earn an annual interest rate of $6$ percent.

b$.$ Recalculate part a using a compounding period that is $(1)$ semiannual and $(2)$ bimonthly.

c$.$ Recalculate parts a and b using a $12$ percent annual interest rate.

d$.$ Recalculate part a using a time horizon of $12$ years at a $6$ percent interest rate.

e$.$ What conclusions can you draw when you compare the answers to parts c and d with the answers to parts a and b$?$