Suppose you are going to receive $$5,000$ per year for $5$ years. The appropriate interest rate is $7$ percent per year.

Requirement $1$:

$($a$)$ What is the present value of the payments if they are in the form of an ordinary annuity $($cash flow starts at the end of the first compounding period$)?$

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$($b$)$ What is the present value if the payments are an annuity due $($cash flow starts at the beginning of the first compounding period$)?q,$

Requirement $2$:

$($a$)$Suppose you plan to invest the payments for $5$ years, what is the future value if the payments are an ordinary annuity?

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$($b$)$Suppose you plan to invest the payments for $5$ years, what is the future value if the payments are an annuity due?

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