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

a$.12\%$ nominal rate, semiannual compounding, discounted back $5$ years. Do not round intermediate calculations. Round your answer to the nearest cent.

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b$.12\%$ nominal rate, quarterly compounding, discounted back $5$ years. Do not round intermediate calculations, Round your answer to the nearest cent.

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c$.12\%$ nominal rate, monthly compounding, discounted back $1$ year. Do not round intermediate calculations. Round your answer to the nearest cent.

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d$.$ Why do the differences in the PVs occur?

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