$($Compound interest with nonannual periods$)$

a$.$ Calculate the future sum of $$2,000,$ given that it will be held in the bank for $10$ years at an APR of $4$ percent.

b$.$ Recalculate part a using compounding periods that are $(1)$ semiannual and $(2)$ bimonthly $($every two months$).$

c$.$ Recalculate parts a and $b$ for an APR of $8$ percent.

d$.$ Recalculate part a using a time horizon of $20$ years $($the APR is still $4$ percent$).$

e$.$ With respect to the effect of changes in the stated interest rate and holding periods on future sums in parts $c$ and $d,$ what conclusions do you draw when you compare these figures with the

answers found in parts a and $b?$