Interest Rates and Equivalence: Master the Fundamentals of Time Value of Money

Question 1

What is the formula to calculate the future value of a single sum of money?

Accepted Answer

FV = PV * (1 + i)^n

Answer

FV = PV * (1 - i)^n

Answer

PV = FV * (1 + i)^n

Answer

PV = FV * (1 - i)^n

Question 2

Which of the following factors does NOT influence the interest rate?

Accepted Answer

The price of gold

Answer

Economic growth

Answer

Inflation

Answer

Government policies

Question 3

What is the fundamental concept of the time value of money?

Accepted Answer

The value of money decreases over time

Answer

The value of money increases over time

Answer

The value of money remains constant over time

Answer

The time value of money is not a valid concept

Question 4

What is the defining characteristic of a perpetuity?

Accepted Answer

A stream of equal, regular cash flows that continue indefinitely

Answer

A one-time payment received at the end of a specific period

Answer

A loan with equal monthly payments but a fluctuating interest rate

Question 5

Which of the following factors does NOT influence interest rates?

Accepted Answer

Consumer demand

Answer

Inflation

Answer

Economic growth

Answer

Fiscal policy

Question 6

The present value of a future cash flow of $1,000 received 5 years from now at an interest rate of 8% is approximately:

Accepted Answer

$793.87

Answer

$831.62

Answer

$925.93

Answer

$1,038.46

Question 7

The future value of a present investment of $1,000 at an interest rate of 7% for a period of 15 years is approximately:

Accepted Answer

$1,219.97

Answer

$1,123.63

Answer

$1,324.85

Answer

$1,438.42

Question 8

Which of the following is an advantage of continuous compounding?

Accepted Answer

Higher future value compared to discrete compounding

Answer

Easier to calculate than discrete compounding

Answer

Eliminates the need for periodic interest payments

Answer

Guarantees a higher return on investment

Question 9

Which formula calculates the future value of a single amount?

Accepted Answer

FV = PV * (1 + r)^n

Answer

FV = PV * (1 - r)^n

Answer

PV = FV * (1 + r)/n

Answer

PV = FV * (1 - r)/n

Question 10

Which formula determines the present value of a single amount?

Accepted Answer

PV = FV / (1 + r)^n

Answer

PV = FV / (1 - r)^n

Answer

FV = PV * (1 + r)/n

Answer

FV = PV * (1 - r)/n

Question 11

Calculate the effective annual interest rate when the nominal interest rate is 10% compounded semi-annually.

Accepted Answer

10.5%

Answer

10.25%

Answer

10.75%

Answer

11%

Question 12

Which factor does NOT influence the time value of money?

Accepted Answer

Risk

Answer

Interest rate

Answer

Inflation

Answer

Investment horizon

Question 13

Which of the following is NOT a type of interest rate used in financial calculations?

Accepted Answer

Discount Factor

Answer

Nominal Interest Rate

Answer

Effective Interest Rate

Answer

Real Interest Rate

Question 14

What is the break-even point in years between two mutually exclusive projects with different cash flows?

Accepted Answer

When the present worths of the projects are equal

Answer

When the future worths of the projects are equal

Answer

When the annual worths of the projects are equal

Answer

When the payback periods of the projects are equal

Question 15

Which formula is used to calculate the future value (FV) of a single sum of money (PV) at an interest rate (r) for (n) years?

Accepted Answer

FV = PV * (1 + r) ^ n

Answer

r = FV / (PV * (1 + n))

Answer

FV = PV / (1 + r) ^ n

Answer

PV = FV / (1 + r) ^ n

Question 16

How does the relationship between interest rates and the present value of a cash flow work?

Accepted Answer

As interest rates increase, the present value of a future cash flow decreases.

Answer

As interest rates increase, the present value of a future cash flow increases.

Answer

Interest rates do not affect the present value of a future cash flow.

Question 17

Which element does NOT influence the equivalence of cash flows?

Accepted Answer

Inflation

Answer

Time period

Answer

Interest rate

Answer

Cash flow amount

Question 18

What formula is used to calculate the internal rate of return (IRR) of a project?

Accepted Answer

IRR = r such that NPV = 0

Answer

IRR = r such that EAW = 0

Answer

IRR = NPV / Initial Investment

Answer

IRR = r such that PV = FV

Question 19

A project with an initial investment of $100,000 is expected to generate the following cash flows:
Year 1: $20,000
Year 2: $30,000
Year 3: $40,000
What is the project's payback period?

Accepted Answer

2.67 years

Answer

4 years

Answer

2 years

Answer

3 years

Question 20

Which investment evaluation method assumes cash flows occur at the end of each period?

Accepted Answer

Present value method

Answer

Internal rate of return method

Answer

Equivalent annual worth method

Answer

Payback period method

Question 21

A project generates the following cash flows: $5,000 in year 1, $6,000 in year 2, and $7,000 in year 3. What is the equivalent annual cash flow (EAC) over the 3-year period, assuming an annual interest rate of 10%?

Accepted Answer

$5,956.86

Answer

$7,000.00

Answer

$5,000.00

Answer

$6,000.00

Question 22

Which of the following is the most appropriate interest rate to use when evaluating capital investment projects that will generate cash flows over multiple years?

Accepted Answer

Weighted average cost of capital (WACC)

Answer

Prime rate

Answer

Risk-free rate

Answer

Current market interest rate

Question 23

A company is considering two mutually exclusive investment options. Option A has an initial cost of $10,000 and generates a cash flow of $2,500 per year for 5 years. Option B has an initial cost of $12,000 and generates a cash flow of $3,000 per year for 5 years. If the company uses a discount rate of 10%, which option is more financially attractive?

Accepted Answer

Option B

Answer

Insufficient information to determine

Answer

Neither option is financially attractive

Answer

Option A

Question 24

Which of the following is an advantage of using present value analysis?

Accepted Answer

It takes into account the time value of money.

Answer

It is complex and difficult to understand.

Answer

It ignores the effects of inflation.

Answer

It cannot be used to compare cash flows occurring at different times.

Question 25

A sinking fund is an investment that is set aside to accumulate funds to repay a loan or other obligation. Which of the following is NOT a characteristic of a sinking fund?

Accepted Answer

The amount invested each period decreases over time.

Answer

The sinking fund is typically invested in conservative assets.

Answer

The interest earned on the fund is considered a part of the sinking fund.

Answer

The sinking fund is established before the obligation is incurred.

Question 26

What is the future worth of $5,000 invested today at an interest rate of 6% per year compounded annually for 10 years?

Accepted Answer

$8,335

Answer

$6,335

Answer

$7,335

Answer

$9,335

Question 27

What is the relationship between the present worth and the future worth of a cash flow?

Accepted Answer

They are equal if the interest rate is zero.

Answer

They are equal regardless of the interest rate.

Answer

The future worth is always greater than the present worth.

Answer

The present worth is always greater than the future worth.

Question 28

Which of the following is a disadvantage of using the payback period as a capital budgeting technique?

Accepted Answer

It does not consider the time value of money.

Answer

It is not reliable.

Answer

It can lead to incorrect investment decisions.

Answer

It is difficult to calculate.

Question 29

What is the annual equivalent of a semi-annual payment of $1,000 if the interest rate is 12% per year compounded semi-annually?

Accepted Answer

$970

Answer

$910

Answer

$1,130

Answer

$1,030

Question 30

Select the correct formula for calculating the future worth of an annuity.

Accepted Answer

FW = P * [(1 + i)^n - 1] / i

Answer

FW = P * i * n

Answer

FW = P * [(1 - i)^n - 1] / i

Answer

FW = P * (1 + i)^n

Question 31

The internal rate of return (IRR) is the interest rate at which the:

Accepted Answer

Net present value is zero

Answer

Equivalent annual worth is zero

Answer

Future worth is zero

Answer

Present worth is zero

Question 32

Which of the following is the most commonly used method for comparing alternative investment options?

Accepted Answer

Net present value

Answer

Return on investment

Answer

Equivalent annual worth

Answer

Payback period

Question 33

You deposit $1,000 in a bank account that earns interest compounded continuously. If the annual interest rate is 5%, how long will it take for your investment to double?

Accepted Answer

13.86 years

Answer

10 years

Answer

15 years

Answer

20 years

Question 34

A company invests $10,000 at an annual compound interest rate of 5%. What will be the future value of the investment after 10 years?

Accepted Answer

$16,288.95

Answer

$15,000

Answer

$17,000

Answer

$18,000

Question 35

An investor wants to invest $20,000 today at an annual compound interest rate to receive $26,000 in 8 years. What is the interest rate?

Accepted Answer

5.01%

Answer

5.5%

Answer

6%

Answer

4.5%

Question 36

A loan with an annual interest rate of 10% is compounded semi-annually. What is the effective annual interest rate?

Accepted Answer

10.25%

Answer

11%

Answer

12%

Answer

9.5%

Question 37

When evaluating investment proposals, which of the following factors should NOT be considered?

Accepted Answer

ROI only

Answer

Time horizon

Answer

Risk

Answer

Availability of funds

Question 38

A project has the following cash flows: -$10,000 (initial investment), $2,000 (Year 1), $3,000 (Year 2), $4,000 (Year 3). Calculate the equivalent annual worth (EAW) of the project over a 3-year period using an interest rate of 12%.

Accepted Answer

$2,228.26

Answer

$2,500

Answer

$2,000

Answer

$3,000

Question 39

Given a nominal interest rate of 6% and an inflation rate of 3%, calculate the real interest rate.

Accepted Answer

2.86%

Answer

9%

Answer

3%

Answer

6%

Question 40

A loan of $10,000 is borrowed at an annual percentage rate (APR) of 10%. If the loan is repaid in equal monthly installments over a 5-year period, calculate the monthly payment.

Accepted Answer

$228.22

Answer

$200

Answer

$300

Answer

$250

Question 41

A bond has a face value of $1,000, a coupon rate of 5%, and a maturity date in 10 years. If the current market interest rate is 6%, determine the price of the bond.

Accepted Answer

$917.43

Answer

$1,000

Answer

$1,200

Answer

$1,100

Question 42

An investment of $5,000 is made today. If the investment earns interest at an annual rate of 7% compounded quarterly, calculate the future worth of the investment in 3 years.

Accepted Answer

$6,172.08

Answer

$6,500

Answer

$5,350

Answer

$7,000

Question 43

A company is considering purchasing a machine that costs \$100,000. The machine is expected to generate annual savings of \$25,000 for 8 years. If the company's MARR is 12%, what is the net present value of the investment?

Accepted Answer

\$78,516

Answer

\$60,000

Answer

\$85,000

Answer

\$90,000

Question 44

Which of the following is a widely used measure of interest rates that reflects the total cost of borrowing over a year, including compounding?

Accepted Answer

Annual Percentage Rate (APR)

Answer

Nominal Interest Rate

Answer

Capital Gain

Answer

Internal Rate of Return (IRR)

Question 45

What is the Future Value of a $1,000 investment at an annual interest rate of 5% compounded annually for 10 years?

Accepted Answer

$1,628.89

Answer

$1,750.00

Answer

$1,500.00

Answer

$1,875.00

Question 46

What is the Present Value of $1,000 to be received 5 years from now, assuming an interest rate of 4% compounded semi-annually?

Accepted Answer

$821.93

Answer

$680.00

Answer

$750.00

Answer

$900.00

Question 47

What is the Present Worth of a project that generates $10,000 in net cash flows at the end of each year for 5 years, assuming an interest rate of 6%? (PMT = $10,000, n = 5, r = 0.06)

Accepted Answer

$42,124.08

Answer

$28,000.00

Answer

$50,000.00

Answer

$36,000.00

Question 48

Which of the following is a limitation of using interest rates in financial analysis?

Accepted Answer

Interest rates may not account for inflation.

Answer

Interest rates are always accurate.

Answer

Interest rates are easy to calculate.

Answer

Interest rates are the only factor to consider in financial decision-making.

Question 49

A project requires an initial investment of $100,000 and is expected to generate annual cash inflows of $25,000 for 6 years. If the discount rate is 10%, what is the net present value (NPV) of the project?

Accepted Answer

$10,166

Answer

-$10,166

Answer

$0

Answer

$150,000

Question 50

Which of the following is NOT a factor that directly influences interest rates?

Accepted Answer

The color of the company's logo

Answer

Supply and demand of capital

Answer

Inflation

Answer

Risk

Question 51

A loan of $5,000 is taken out at an annual interest rate of 8% compounded monthly. What is the effective annual interest rate (EAR) of this loan, rounded to two decimal places?

Accepted Answer

8.30%

Answer

8.16%

Answer

8.50%

Answer

8.00%

Question 52

Which of the following best describes an annuity?

Accepted Answer

A series of equal payments made over a set period of time.

Answer

A payment made at the end of a loan term.

Answer

A single lump sum payment.

Answer

A series of unequal payments.

Question 53

A company is considering two mutually exclusive projects, Project A and Project B. Both projects have a 5-year life and require an initial investment of $100,000. Project A is expected to generate annual cash inflows of $30,000, while Project B is expected to generate annual cash inflows of $25,000. The discount rate is 12%. Which project should the company choose based on the higher net present value (NPV)?

Accepted Answer

Project A

Answer

Both projects are equally desirable

Answer

Neither project is financially viable

Answer

Project B

Question 54

What is the present value of $10,000 received in 5 years at a discount rate of 6%, rounded to the nearest dollar?

Accepted Answer

$7,472

Answer

$13,382

Answer

$10,000

Answer

$6,000

Question 55

A bond with a face value of $1,000, a coupon rate of 5%, and a maturity of 10 years is currently trading at a price of $950. Assuming annual coupon payments, what is the approximate yield to maturity (YTM) of the bond, rounded to two decimal places?

Accepted Answer

5.53%

Answer

6.00%

Answer

4.50%

Answer

5.00%

Question 56

Which of the following statements is TRUE regarding the relationship between interest rates and the time value of money?

Accepted Answer

Higher interest rates generally lead to a higher time value of money.

Answer

Interest rates have no impact on the time value of money.

Answer

Lower interest rates generally lead to a higher time value of money.

Question 57

A company is considering purchasing a machine that costs $50,000. The machine is expected to have a useful life of 5 years and a salvage value of $5,000. The company's required rate of return is 15%. What is the annual equivalent cost (AEC) of the machine, rounded to the nearest dollar?

Accepted Answer

$14,286

Answer

$15,000

Answer

$10,000

Answer

$12,500