Problem $5\mathrm{.}23($Future Value for Various Compounding Periods$)$

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Find the amount to which $$800$ will grow under each of these conditions:

a$.16\%$ compounded annually for $4$ years. Do not round intermediate calculations. Round your answer to the nearest cent.

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b$.16\%$ compounded semiannually for $4$ years. Do not round intermediate calculations. Round your answer to the nearest cent.

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c$.16\%$ compounded quarterly for $4$ years. Do not round intermediate calculations. Round your answer to the nearest cent.

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d$.16\%$ compounded monthly for $4$ years. Do not round intermediate calculations. Round your answer to the nearest cent.

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e$.16\%$ compounded daily for $4$ 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?