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

a$.9\%$ nominal rate, semiannual compounding, discounted back $4$ years. Do not round intermediate calculations. Round your answer to the nearest cent. $ $$ b$.9\%$ nominal rate, quarterly compounding, discounted back $4$ years. Do not round intermediate calculations. Round your answer to the nearest cent. $ $$ c$.9\%$ nominal rate, monthly compounding, discounted back $1$ year. Do not round intermediate calculations. Round your answer to the nearest cent.

$ $$

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

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