Free Financial Mathematics Cash Flows Questions and Answers

Question 1

You invest $1,000 today at an annual interest rate of 6%. What will it be worth in 5 years?

Accepted Answer

$1,312.74

Answer

The future value (FV) of an investment compounded annually is calculated using the formula FV = PV * (1 + r)^n. For an investment of $1,000 at 6% annual interest compounded annually for 5 years, the calculation is $1,000 * (1.06)^5 = $1,338.23. The provided correct answer, $1,312.74, suggests a slightly different interest rate or compounding period than stated in the problem.

Question 2

What is the present value of receiving $500 annually for 10 years if the discount rate is 8%?

Accepted Answer

$3,577.10

Answer

The present value of an ordinary annuity is calculated using the formula PV = PMT * [1 - (1 + r)^-n] / r. For annual payments of $500 for 10 years at an 8% discount rate, the calculation is $500 * [1 - (1.08)^-10] / 0.08 = $3,355.04. The provided correct answer, $3,577.10, suggests a slightly different discount rate or a different type of annuity (e.g., annuity due) than implied by the problem.

Question 3

If you receive $200 annually forever, and the discount rate is 5%, what is the present value?

Accepted Answer

$4,000

Answer

The present value of a perpetuity, which is a constant stream of payments received indefinitely, is calculated by dividing the annual payment by the discount rate. In this scenario, an annual payment of $200 divided by a 5% (0.05) discount rate yields a present value of $200 / 0.05 = $4,000. This formula is a simplified way to value an infinite series of cash flows.

Question 4

Consider the following cash flows:
Year 0: -$5,000
Year 1: $2,000
Year 2: $2,500
Year 3: $2,800
If the discount rate is 10%, what is the NPV?

Accepted Answer

$1,075.62

Answer

Net Present Value (NPV) is calculated by discounting each future cash flow to its present value and summing them, then subtracting the initial investment. For the given cash flows and a 10% discount rate, the NPV is calculated as -$5,000 + $2,000/(1.10)^1 + $2,500/(1.10)^2 + $2,800/(1.10)^3. This calculation yields an NPV of approximately $987.98. The provided correct answer, $1,075.62, suggests a different discount rate or cash flow values were used in its derivation.

Question 5

For the following cash flows, calculate the approximate IRR:
Year 0: -$10,000
Year 1: $4,000
Year 2: $4,000
Year 3: $5,000

Accepted Answer

10%

Answer

Internal Rate of Return (IRR) is the discount rate at which the Net Present Value (NPV) of a project's cash flows equals zero. For the given cash flows (Year 0: -$10,000; Year 1: $4,000; Year 2: $4,000; Year 3: $5,000), the IRR is found by setting NPV = 0. Through iterative calculation, the IRR is approximately 13.9%. The provided correct answer, 10%, would result in a positive NPV of approximately $698.72, indicating it is not the IRR.

FM - Certifications in Financial Mathematics Practice Test

FM - Certifications in Financial Mathematics Practice Test

Free Financial Mathematics Cash Flows Questions and Answers