Question

An investment offers $5,500 per year, with the first payment occurring one year from now. The required return is 7 percent.

a.	What would the value be today if the payments occurred for 20 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

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

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

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

Answer 1

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

=$5500[1-(1.07)^-20]/0.07

=5500*10.59401425

=$58267.08(Approx).

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

=$5500[1-(1.07)^-45]/0.07

=5500*13.60552159

=$74830.37(Approx).

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

=$5500[1-(1.07)^-70]/0.07

=5500*14.16038934

=$77,882.14(Approx).

d.Present value of perpetuity=Annual inflows/required return

=(5500/0.07)

which is equal to

=$78571.43(Approx).