Question

An investment offers $5,200 per year for 20 years, with the first payment occurring one year from now.

If the required return is 7 percent, what is the value of the investment today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

What would the value today be if the payments occurred for 45 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

What would the value today be if the payments occurred for 70 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

What would the value today be if the payments occurred forever?

Answer 1

a.Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

=5200[1-(1.07)^-20]/0.07

=5200*10.59401425

=$55088.87(Approx).

b.Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

=5200[1-(1.07)^-45]/0.07

=5200*13.60552159

=$70748.71(Approx).

c.Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

=5200[1-(1.07)^-70]/0.07

=5200*14.16038934

=$73634.02(Approx).

d.Present value of perpetuity=Annual cash flows/required return

=(5200/0.07)

=$74285.71(Approx).