Find the future values of the following ordinary annuities:

FV of $$500$ paid each $6$ months for $5$ years at a nominal rate of $11\%$ compounded semiannually. Do not round intermediate calculations. Round your answer to the nearest cent.

$

FV of $$250$ paid each $3$ months for $5$ years at a nominal rate of $11\%$ compounded quarterly. Do not round intermediate calculations. Round your answer to the nearest cent.

$

These annuities receive the same amount of cash during the $5-$year period and earn interest at the same nominal rate, yet the annuity in part b ends up larger than the one in part a$.$ Why does this occur?

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