Suppose you are going to receive $$12,000$ per year for five years. The appropriate interest rate is $9$ percent.

a$-1.$ What is the present value of the payments if they are in the form of an ordinary annuity?

Note: Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$ a$-2.$ What is the present value of the payments if the payments are an annuity due?

Note: Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$ b$-1.$ Suppose you plan to invest the payments for five years. What is the future value if the payments are an ordinary annuity?

Note: Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$ b$-2.$ What is the future value if the payments are an annuity due?

Note: Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

c$-1.$ Which has the higher present value, the ordinary annuity or annuity due?

c$-2.$ Which has the higher future value?

$\backslash$table$[[$a$-1.$ Present value of ordinary annuity,$],[$a$-2.$ Present value of annuity due,$],[$b$-1.$ Future value of ordinary annuity,$],[$b$-2.$ Future value of annuity due,$],[$c$-1.$ Higher present value,$],[$c$-2.$ Higher future value,$]]$

Suppose you are going to receive $$12,000$ per year for five years. The appropriate interest rate is $9$ percent.

a$-1.$ What is the present value of the payments if they are in the form of an ordinary annuity?

Note: Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$ a$-2.$ What is the present value of the payments if the payments are an annuity due?

Note: Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$ b$-1.$ Suppose you plan to invest the payments for five years. What is the future value if the payments are an ordinary annuity? Note: Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$ b$-2.$ What is the future value if the payments are an annuity due?

Note: Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

c$-1.$ Which has the higher present value, the ordinary annuity or annuity due?

c$-2.$ Which has the higher future value?

$\backslash$table$[[$a$-1.$ Present value of ordinary annuity,$$,46,675\mathrm{.}82$