Problem $28-18($Future Value of an Annuity for Various Compounding Periods$)$

Future Value of an Annuity for Various Compounding Periods

Find the future values of the following ordinary annuities.

a$.$ FV of $$200$ paid each $6$ months for $10$ years at a nominal rate of $16\%,$ compounded semiannually. Do not round intermediate calculations. Round your answer to the nearest cent.

$

b$.$ FV of $$100$ paid each $3$ months for $10$ years at a nominal rate of $16\%,$ compounded quarterly. Do not round intermediate calculations. Round your answer to the nearest cent.

$

c$.$ The annuities described in parts a and $b$ have the same amount of money paid into them during the $10-$year period, and both earn interest at the same nominal rate, yet the annuity in part b earns more than the one in part a over the $10$ years. Why does this occur?