An investment offers $6,600 per year for 10 years, with the first payment occurr
ID: 2612552 • Letter: A
Question
An investment offers $6,600 per year for 10 years, with the first payment occurring one year from now.
If the required return is 5 percent, what is the value of the investment? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.)
Present value $
What would the value be if the payments occurred for 35 years? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.)
Present value $
What would the value be if the payments occurred for 65 years? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.)
Present value $
What would the value be if the payments occurred forever? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.)
Present value $
Explanation / Answer
Amount payable per annum A = $ 6600
required rate of return i = 5% or 0.05
Period of annuity payment n = 10 years
Present Value of an annuity can be calculated using the formula
P = A * PVAF(i,n) where
PVAF(i,n) = {1-1/(1+i)^n}/i
Substituting the values of i and n in the above
PVAF(5,10) = {1-1/(1+.05)^10)}/0.05 = {1- 1/1.05^10}/0.05 = {1-1/1.62889463}/0.05
= {1- 0.61391325}/0.05 = 0.38608675/0.05 = 7.721735
Present Value P = 6600 * 7.721735 = $ 50,963.451 or $ 50,963.45
Answer to Part II
Period of annuity payments n = 35 years
PVAF(5,35) = {1-1/(1+.05)^35)}/0.05 = {1-1/1.05^35}/0.05 = {1-1/5.51601537}/0.05
= {1- 0.181290285}/0.05 = 0.818709715/0.05 = 16.3741943
Present Value P = 6600 * 16.3741943 = $ 108,069.68238 or $ 108,069.68
Answer to Part III
Period of annuity paymenets n = 65 years
PVAF(5,65) = {1-1/(1+.05)^65)}/0.05 = {1-1/1.05^65}/0.05 = {1-1/23.83990056}/0.05
= {1-0.041946484}/0.05 = 0.958053516/0.05 = 19.16107032
Present Value P = 6600 * 19.16107032 = $ 126,463.064112 or $ 126,463.06
Answer to Part IV
Period of Annuity = Perpetual
Present Value of Annuity can be calculated by using the formula
P = A/i = 6600 / 0.05 = $ 132,000
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