Suppose you are going to receive $$25,000$ per year for $10$ year. The appropriate interest rate is $5\%.$

$($a$)$ What is the present value of these payments if they are an ordinary annuity?

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$($b$)$ What is the present value of these payments if they are an annuity due?

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$($c$)$ If you invest the payments over these $10$ years, what will be their future value if they are an ordinary annuity?

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$($d$)$ If you invest the payments over these $10$ years, what will be their future value if they are an annuity due?

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