Find the future values of the following ordinary annuities.

Payments of $$600$ every $6$ months for $8$ years at a nominal rate of $12\%,$ compounded semiannually. Do not round intermediate calculations. Round your answer to the nearest cent.

$

Payments of $$300$ every $3$ months for $8$ years at a nominal rate of $12\%,$ compounded quarterly. Do not round intermediate calculations. Round your answer to the nearest cent.

$

The annuities described in parts a and b have the same total amount of money paid into them during the $8-$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 $8$ years. Why does this occur?