You are comparing two investment options that each pay 5 percent interest, compounded annually. both options will provide you with $12,000 of income. option a pays three annual payments starting with $2,000 the first year followed by two annual payments of $5,000 each. option b pays three annual payments of $4,000 each. which one of the following statements is correct given these two investment options?
a. both options are of equal value given that they both provide $12,000 of income. b. option a has the higher future value at the end of year three. c. option b has a higher present value at time zero than does option a. d. option b is a perpetuity. e. option a is an annuity.

Option (C) is correct

Explanation:

Both investments pay 5% interest and income of $12,000.

option A gives annual payment of $2,000 in first three years and $5,000 in the next two years.

Option B pays $4,000 annually for three years

Future value of option A at the end of third year = 2000 × 1.1236 (FV factor) + 5000 × 1.06 + 5000 = $12,547.20

Future value of option B at the end of third year = 4000× 3.1525 (FV factor of annuity) = $12,610

Option B has higher future value, so option B is incorrect.

Present value of option A  = 2000 × 0.9434 (PV factor) + 5000 × 0.89 + 5000 × 0.8396 = $10,534

Present value of option B  = 4000× 2.673 (PV factor of annuity) = $10,692

Therefore, option B has higher present value at time 0 as compared to option A, so option (C) is correct.

Option B is not a perpetuity as life of investment is definite that is 3 years and option A is not an annuity as cash inflow is not same every year.

c is the correct answer.