Problem $5\mathrm{.}24($Present Value for Various Discounting Periods$)$

Find the present value of $$200$ due in the future under each of these conditions:

a$.15\%$ nominal rate, semiannual compounding, discounted back $4$ years. Do not round intermediate calculations. Round your answer to the nearest cent.

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b$.15\%$ nominal rate, quarterly compounding, discounted back $4$ years. Do not round intermediate calculations. Round your answer to the nearest cent.

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c$.15\%$ 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?

$-$Select$-$

The present values decline as periods per year increase.

The present values decline as periods per year decrease.

The present values increase as periods per year increase.

The present values are not affected by changes in the number of periods per year.

The present values are positively related to the number of discounting periods per year.