Find the future values of the following ordinary annuities.

FV of $800 each 6 months for 10 years at a nominal rate of 8%, compounded semiannually. Do not round intermediate calculations. Round your answer to the nearest cent.

FV of $400 each 3 months for 10 years at a nominal rate of 8%, 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 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?