Problem $5\mathrm{.}2$: Assume the company you work for had a great year and as a result you were awarded a $$5,000$ bonus for all of your hard work.

a$.$ Calculate the future value of the $$5,000$ if it will be held in a corporate bond fund for $10$ years and earned an annual compound interest rate of $4\mathrm{.}5\%.$

b$.$ Recalculate part $\text{'}$a$\text{'}$ using a compounding period that is $(1)$ quarterly; and $(2)$ monthly.

c$.$ Why are the values in part $\text{'}$b$\text{'}$ larger than part $\text{'}$a$\text{'}?$