Find the present value of $$500$ due in the future under each of these conditions:

$9\%$ nominal rate, semiannual compounding, discounted back $8$ years. Do not round intermediate calculations. Round your answer to the nearest cent.

$

$9\%$ nominal rate, quarterly compounding, discounted back $8$ years. Do not round intermediate calculations. Round your answer to the nearest cent.

$

$9\%$ nominal rate, monthly compounding, discounted back $1$ year. Do not round intermediate calculations. Round your answer to the nearest cent.

$

Why do the differences in the PVs occur?