Find the amount to which $$500$ will grow under each of these conditions:

a$.6\%$ compounded annually for $7$ years. Do not round intermediate calculations. Round your answer to the nearest cent.

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b$.6\%$ compounded semiannually for $7$ years. Do not round intermediate calculations. Round your answer to the nearest cent.

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c$.6\%$ compounded quarterly for $7$ years. Do not round intermediate calculations. Round your answer to the nearest cent. $

d$.6\%$ compounded monthly for $7$ years. Do not round intermediate calculations. Round your answer to the nearest cent.

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e$.6\%$ compounded daily for $7,$years. Assume $365-$days in a year. Do not round intermediate calculations. Round your answer to the nearest cent. $

f$.$ Why does the observed pattern of FVs occur?