You are comparing two investment options that each pay 6% interest, compounded annually. Both options will provide you with $12,000 of income. Option A pays $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? Assume a positive discount rate. Both options are of equal value since they both provide $12,000 of income. a. Option A has the higher future value at the end of year three.

b. Option B has a higher present value at time zero.

c. Option B is a perpetuity.

d. Option A is an annuity.

Question

Business

Eliezer Gonzales

18 November, 04:42

You are comparing two investment options that each pay 6% interest, compounded annually. Both options will provide you with $12,000 of income. Option A pays $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? Assume a positive discount rate. Both options are of equal value since they both provide $12,000 of income. a. Option A has the higher future value at the end of year three.

b. Option B has a higher present value at time zero.

c. Option B is a perpetuity.

d. Option A is an annuity.

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Answers (1)

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Sierra Wolf · Answer 1

B) Option B has a higher present value at time zero.

Explanation:

the present value of option A = ($2,000 / 1.06) + ($5,000 / 1.06²) + ($5,000 / 1.06³) = $1,886.79 + $4,449.98 + $4,198.10 = $10,534.87

the present value of option B = ($4,000 / 1.06) + ($4,000 / 1.06²) + ($4,000 / 1.06³) = $3,773.58 + $3,559.99 + $3,358.48 = $10,692.05

present value of option B ($10,692.05) is higher than the present value of option A ($10,534.87)