Find the amount to which $$400$ will grow under each of these conditions:

a$.4\%$ compounded annually for $3$ years. Do not round intermediate calculations. Round your answer to the nearest cent.

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b$.4\%$ compounded semiannually for $3$ years. Do not round intermediate calculations. Round your answer to the nearest cent.

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c$.4\%$ compounded quarterly for $3$ years. Do not round intermediate calculations. Round your answer to the nearest cent.

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d$.4\%$ compounded monthly for $3$ years. Do not round intermediate calculations. Round your answer to the nearest cent.

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e$.4\%$ compounded daily for $3$ years. Assume $365-$days in a year. Do not round intermediate calculations, Round your answer to the nearest cent.

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