Suppose you are going to receive $$16,000$ per year for $8$ years. The appropriate interest rate is $7$ percent.

a$.$ What is the present value of the payments if they are in the form of an ordinary annuity?

b$.$ What is the present value if the payments are an annuity due?

c$.$ Suppose you plan to invest the payments for $8$ years, what is the future value if the payments are an ordinary annuity?

d$.$ Suppose you plan to invest the payments for $8$ years, what is the future value if the payments are an annuity due?