Free Financial Mathematics Time Value of Money Questions and Answers

Question 1

If you invest $2,000 today at an annual interest rate of 6%, compounded annually, what will the investment be worth in 4 years?

Accepted Answer

$2,673.84

Answer

The future value (FV) of an investment compounded annually is calculated using the formula FV = PV * (1 + r)^n. For an investment of $2,000 at 6% annual interest compounded annually for 4 years, the calculation is $2,000 * (1.06)^4 = $2,524.95. The provided correct answer, $2,673.84, would be the future value if the investment period were approximately 5 years instead of 4 years.

Question 2

What is the present value of $8,000 to be received 6 years from now, with a discount rate of 7% annually?

Accepted Answer

$5,394.94

Answer

The present value (PV) of a future sum is calculated using the formula PV = FV / (1 + r)^n. For $8,000 to be received in 6 years with a 7% annual discount rate, the calculation is $8,000 / (1.07)^6 = $5,330.79. The provided correct answer, $5,394.94, suggests a slightly different discount rate or rounding in the problem's parameters.

Question 3

You borrow $15,000 to be repaid over 5 years with an annual interest rate of 9%, compounded annually. What is the annual payment?

Accepted Answer

Answer

This question requires calculating the annual payment for an amortizing loan, which is an annuity payment. The formula used is PMT = [PV * r] / [1 - (1 + r)^-n], where PV is the loan amount ($15,000), r is the annual interest rate (0.09), and n is the number of years (5). Plugging in these values yields an annual payment of approximately $3,856.59, making option A the correct answer.

Question 4

If a perpetuity pays $1,000 annually and the discount rate is 5%, what is the value of the perpetuity?

Accepted Answer

$20,000.00

Answer

The value of a perpetuity, which is a stream of equal payments that continues indefinitely, is calculated by dividing the annual payment by the discount rate. In this case, an annual payment of $1,000 divided by a 5% (0.05) discount rate yields a perpetuity value of $1,000 / 0.05 = $20,000. This formula provides the present value of an infinite series of cash flows.

Question 5

What is the future value of an annuity that pays $2,000 annually for 10 years at an interest rate of 8%?

Accepted Answer

$28,973.00

Answer

The future value of an ordinary annuity is calculated using the formula FV = PMT * [((1 + r)^n - 1) / r]. Here, PMT is $2,000, r is 8% (0.08), and n is 10 years. Plugging these values into the formula yields $2,000 * [((1.08)^10 - 1) / 0.08], which calculates to approximately $28,973.12. This closely matches option A.

FM - Certifications in Financial Mathematics Practice Test

FM - Certifications in Financial Mathematics Practice Test

Free Financial Mathematics Time Value of Money Questions and Answers