APPENDIX: Test BAnk

tIME vALUE OF MONEY

APPENDIX LEARNING OBJECTIVES

1. Compute interest and future values. Simple interest is computed on the principal only, while compound interest is computed on the principal and any interest earned that has not been withdrawn.

To solve for future value of a single amount, prepare a time diagram of the problem. Identify the principal amount, the number of compounding periods, and the interest rate. Using the future value of 1 table, multiply the principal amount by the future value factor specified at the intersection of the number of periods and the interest rate.

To solve for future value of an annuity, prepare a time diagram of the problem. Identify the amount of the periodic payments (receipts), the number of payments, and the interest rate. Using the future value of an annuity of 1 table, multiply the amount of the payments by the future value factor specified at the intersection of the number of periods and the interest rate.

2. Compute present values. The following three variables are fundamental to solving present value problems: (1) the future amount, (2) the number of periods, and (3) the interest rate (the discount rate).

To solve for present value of a single amount, prepare a time diagram of the problem. Identify the future amount, the number of discounting periods, and the discount (interest) rate. Using the present value of a single amount table, multiply the future amount by the present value factor specified at the intersection of the number of periods and the discount rate.

To solve for present value of an annuity, prepare a time diagram of the problem. Identify the amount of future periodic receipts or payment (annuities), the number of discounting periods, and the discount (interest) rate. Using the present value of an annuity of 1 table, multiply the amount of the annuity by the present value factor specified at the intersection of the number of periods and the interest rate.

To compute the present value of notes and bonds, determine the present value of the principal amount: Multiply the principal amount (a single future amount) by the present value factor (from the present value of 1 table) intersecting at the number of periods (number of interest payments) and the discount rate. To determine the present value of the series of interest payments: Multiply the amount of the interest payment by the present value factor (from the present value of an annuity of 1 table) intersecting at the number of periods (number of interest payments) and the discount rate. Add the present value of the principal amount to the present value of the interest payments to arrive at the present value of the note or bond.

3. Compute the present value in capital budgeting situations. Compute the present values of all cash inflows and all cash outflows related to the capital budgeting proposal (an investment-type decision). If the net present value is positive, accept the proposal (make the investment). If the net present value is negative, reject the proposal (do not make the investment).

4. Use technological tools to solve time value of money problems. Technological tools, such as financial calculators and Excel, can be used to solve the same and additional problems as those solved with time value of money tables. When using a financial calculator, you will enter into the financial calculator the amounts for all of the known elements of a time value of money problem (periods, interest rate, payments, future or present value), and it solves for the unknown element. Particularly useful situations involve interest rates and compounding periods not presented in the tables. When using Excel, each function will require some combination of the following inputs: Rate, Nper, Pmt, PV or FV, and Type. The advantage of Excel is that it allows users to quickly modify inputs to understand how changes in inputs such as the interest rate might impact the present value.

Difficulties:

Easy: 29

Medium: 50

Hard: 0

Question List by Section

Interest and Future Values

Nature of Interest: 1

Simple Interest

Compound Interest: 2, 13

Future Value of a Single Amount: 3, 14,, 15, 16, 17, 46, 47, 48, 49, 50

Future Value of an Annuity: 4. 18, 19, 20, 21, 22, 51, 52, 53, 54, 55 56, 75, 76

Present Values

Present Value Variables: 5, 6, 23, 24, 25, 77

Present Value of a Single Amount: 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 57, 58, 59, 60, 61, 62, 63

Present Value of an Annuity: 7, 9, 37, 38, 40, 41, 64, 65, 66, 67, 68, 69, 70, 71

Time Periods and Discounting: 30

Present Value of a Long-term Note or Bond: 8, 39, 42, 72, 78

Capital Budgeting Situations: 10, 11, 43, 44, 73

Using Technological Tools: 12, 45, 74

TRUE-FALSE STATEMENTS

1. Interest is the difference between the amount borrowed and the principal.

2. Compound interest is computed on the principal and any interest earned that has not been paid or received.

3. The future value of a single amount is the value at a future date of a given amount invested now, assuming compound interest.

4. When the periodic payments are not equal in each period, the future value can be computed by using a future value of an annuity table.

5. The process of determining the present value is referred to as discounting the future amount.

6. A higher discount rate produces a higher present value.

7. In computing the present value of an annuity, it is not necessary to know the number of discount periods.

8. The present value of a long-term note or bond is a function of two variables.

9. The present value of an annuity is the value now of a series of future receipts or payments, discounted assuming compound interest.

10. The decision to make long-term capital investments is best evaluated without recognizing the time value of money.

11. In a capital budgeting decision, a positive net present value means the decision to invest should be accepted.

12. With Excel or a financial calculator, one can solve for any interest rate or for any number of periods in a time value of money problem.

MULTIPLE-CHOICE QUESTIONS

Note: Students will need future value and present value tables for some questions.

13. Compound interest is the return on principal

a. only.

b. for one or more periods.

c. plus interest for two or more periods.

d. for one period.

14. The factor 1.08160 is taken from the 4% column and 2 periods row in a certain table. From what table is this factor taken?

a. Future value of 1

b. Future value of an annuity of 1

c. Present value of 1

d. Present value of an annuity of 1

15. If $40,000 is put in a savings account paying interest of 4% compounded annually, what amount will be in the account at the end of 5 years?

a. $32,878

b. $48,000

c. $48,620

d. $48,666

16. The future value of 1 factor will always be

a. equal to 1.

b. greater than 1.

c. less than 1.

d. equal to the interest rate.

17. All of the following are necessary to compute the future value of a single amount except the

a. interest rate.

b. number of periods.

c. principal.

d. maturity value.

18. Which table has a factor of 1.00000 for 1 period at every interest rate?

a. Future value of 1

b. Future value of an annuity of 1

c. Present value of 1

d. Present value of an annuity of 1

19. Acme Company deposits $20,000 in a fund at the end of each year for 5 years. The fund pays interest of 4% compounded annually. The balance in the fund at the end of 5 years is computed by multiplying

a. $20,000 by the future value of 1 factor.

b. $100,000 by 1.04.

c. $100,000 by 1.20.

d. $20,000 by the future value of an annuity factor.

20. The future value of an annuity factor for 2 periods is equal to

a. 1 plus the interest rate.

b. 2 plus the interest rate.

c. 2 minus the interest rate.

d. 2.

21. If $30,000 is deposited in a savings account at the end of each year and the account pays interest of 5% compounded annually, what will be the balance of the account at the end of 10 years?

a. $48,867

b. $315,000

c. $377,337

d. $450,000

22. Which of the following is not necessary to know in computing the future value of an annuity?

a. Amount of the periodic payments

b. Interest rate

c. Number of compounding periods

d. Year the payments begin

23. In present value calculations, the process of determining the present value is called

a. allocating.

b. pricing.

c. negotiating.

d. discounting.

24. Present value is based on the

a. dollar amount to be received.

b. length of time until the amount is received.

c. interest rate.

d. All of the answers are correct.

25. Which of the following accounting problems does not involve a present value calculation?

a. The determination of the market price of a bond.

b. The determination of the declining-balance depreciation expense.

c. The determination of the amount to report for long-term notes payable.

d. The determination of the amount to report for lease liability.

26. If you can earn an 8% rate of return, what amount would you need to invest to have $30,000 one year from now?

a. $27,747

b. $27,778

c. $27,273

d. $29,700

27. If you can earn a 15% rate of return, what amount would you need to invest to have $15,000 one year from now?

a. $14,852

b. $13,125

c. $12,750

d. $13,044

28. If the single amount of $2,000 is to be received in 2 years and discounted at 11%, its present value is

a. $1,818.

b. $1,623.

c. $1,802.

d. $2,754.

29. If the single amount of $3,000 is to be received in 3 years and discounted at 6%, its present value is

a. $2,519.

b. $2,830.

c. $2,600.

d. $2,820.

30. Which of the following discount rates will produce the smallest present value?

a. 8%

b. 9%

c. 10%

d. 4%

31. Suppose you have a winning lottery ticket and are given the option of accepting $3,000,000 three years from now or taking the present value of the $3,000,000 now. The sponsor of the prize uses a 6% discount rate. If you elect to receive the present value of the prize now, the amount you will receive is

a. $2,518,860.

b. $2,591,520.

c. $2,670,000.

d. $3,000,000.

32. The amount you must deposit now in your savings account, paying 6% interest, to accumulate $6,000 for a down payment 5 years from now on a new car is

a. $1,200.

b. $4,484.

c. $4,477.

d. $4,200.

33. The amount you must deposit now in your savings account, paying 5% interest, to accumulate $10,000 for your first tuition payment when you start college in 3 years is

a. $8,500.

b. $7,830.

c. $8,638.

d. $8,860.

34. The present value of $10,000 to be received in 5 years will be smaller if the discount rate is

a. increased.

b. decreased.

c. not changed.

d. equal to the stated rate of interest.

35. If Kim Kardashian invests $10,514.81 now and she will receive $30,000 at the end of 11 years, what annual rate of interest will she be earning on her investment?

a. 8%

b. 8.5%

c. 9%

d. 10%

36. Katy Perry has been offered the opportunity of investing $73,540 now. The investment will earn 8% per year and at the end of its life will return $200,000 to Katy. How many years must Katy wait to receive the $200,000?

a. 10

b. 11

c. 12

d. 13

37. Ryan Seacrest invests $35,516.80 now for a series of $5,000 annual returns beginning one year from now. Ryan will earn 10% on the initial investment. How many annual payments will Ryan receive?

a. 10

b. 12

c. 13

d. 15

38. In order to compute the present value of an annuity, it is necessary to know the

1. discount rate.

2. number of discount periods and the amount of the periodic payments or receipts.

a. 1

b. 2

c. both 1 and 2

d. something in addition to 1 and 2

39. A $10,000, 6%, 5-year note payable that pays interest quarterly would be discounted back to its present value by using tables that would indicate which one of the following period-interest combinations?

a. 5 interest periods, 6% interest

b. 20 interest periods, 6% interest

c. 20 interest periods, 1.5% interest

d. 5 interest periods, 1.5% interest

40. A1 Service Company has just purchased equipment that requires annual payments of $40,000 to be paid at the end of each of the next 4 years. The appropriate discount rate is 15%. What is the present value of the payments?

a. $114,199

b. $160,000

c. $46,975

d. $150,135

41. Acme Wholesale Company has purchased equipment that requires annual payments of $30,000 to be paid at the end of each of the next 6 years. The appropriate discount rate is 12%. What amount will be used to record the equipment?

a. $180,000

b. $123,342

c. $165,772

d. $115,650

42. The selling price of a $1,000,000, ten-year, 12% bond that pays interest semi-annually and which was sold to yield an effective rate of 10% is

a. $1,122,890.

b. $1,124,623.

c. $1,133,270.

d. $1,872,360.

Use Tables 3 and 4.

43. Ace Supply Company is considering an investment in equipment. The present value of cash inflows includes

a. the present value of annual net operating cash flows and the present value of the salvage value.

b. the present value of annual net operating cash flows, but not the present value of the salvage value.

c. neither the present value of annual net operating cash flows nor the present value of the salvage value.

d. the present value of the salvage value, but not the present value of annual net operating cash flows.

44. Acme Discount Retail Company is considering purchasing equipment. The equipment will produce the following cash flows:

Year 1 $120,000

Year 2 $200,000

Ace requires a minimum rate of return of 10%. What is the maximum price Dexter should pay for this equipment?

a. $274,381

b. $165,290

c. $320,000

d. $160,000

45. Which can be computed using Excel or a financial calculator?

a. the future value of a single sum and the future value of an annuity.

b. the future value of a single sum but not the future value of an annuity.

c. neither the future value of a single sum nor the future value of an annuity.

d. the future value of an annuity but not the future value of a single sum.

Exercises

Ex. 46

Katy Perry deposited $10,000 in an account paying interest of 4% compounded annually. What amount will be in the account at the end of 4 years?

Ex. 47

Acme Company borrowed $90,000 on January 2, 2025. This amount plus accrued interest of 6% compounded annually will be repaid at the end of 3 years. What amount will Acme repay at the end of the third year?

Ex. 48

A1 Service Company has decided to begin accumulating a fund for plant expansion. The company deposited $80,000 in a fund on January 2, 2025. A1 will also deposit $40,000 annually at the end of each year, starting in 2025. The fund pays interest at 4% compounded annually. What is the balance of the fund at the end of 2029 (after the 2029 deposit)?

Ex. 49

Kim Kardashian plans to buy an automobile and can deposit $3,000 toward the purchase today. If the annual interest rate is 8%, how much can Mandy expect to have as a down payment in 3 years?

Ex. 50

Luke Bryan plans to buy a home and can deposit $15,000 for the purchase today. If the annual interest rate is 8%, how much can Luke expect to have for a down payment in 5 years?

Ex. 51

Meghan Markle and Prince Harry plan to invest $2,500 a year in an educational IRA for their daughter, Lilibet. They will make these deposits on December 31 of each year. Meghan and Harry feel they can safely earn 8%. How much will be in this account on December 31 of the 18^th year?

Ex. 52

Matt Damon acquired a bad habit of smoking in high school. Matt spends approximately $70 a month or $840 a year on cigarettes. He is not concerned with health issues, but he is keenly aware of financial issues. Show Matt how much he would have at retirement in 20 years if he invested $840 a year at 8% instead of smoking.

Ex. 53

The cost of Katy Perry’s phone is $40 a month. She can upgrade to the newest model for an additional $10 a month ($120 a year). Katy thinks it would be “cool” to have the latest model and after all $10 a month is not so much. Show Katy how much she will have in 20 years if she invests this $120 a year at 9% instead of accepting the upgrade.

Ex. 54

Acme Company deposited $15,000 annually for 6 years in an account paying 5% interest compounded annually. What is the balance of the account at the end of the 6th year?

Ex. 55

A1 Company issued $900,000, 10-year bonds and agreed to make annual sinking fund deposits of $72,000. The deposits are made at the end of each year to a fund paying 5% interest compounded annually. What amount will be in the sinking fund at the end of the 10 years?

Ex. 56

Compute the future value of $6,000 invested every year at an interest rate of 9%. You invest the money for 20 years with the first payment made at the end of the year.

Ex. 57

Ace Service Company is considering an investment that will return a lump sum of $2,500,000 six years from now. What amount should Ace pay for this investment to earn an 11% return?

Ex. 58

Acme Supply Company earns 12% on an investment that will return $400,000 eleven years from now. What is the amount Acme should invest now to earn this rate of return?

Ex. 59

If Lionel Richie invests $11,970 now, he will receive $40,000 at the end of 14 years. What annual rate of return will Lionel earn on his investment?

Ex. 60

Ryan Seacrest wants to buy a car in 3 years. He will need $3,000 for a down payment. The annual interest rate is 9%. How much money must Ryan invest today for the purchase?

Ex. 61

Meghan Markle plans to buy a surround sound stereo system for $1,100 after 3 years. If the interest rate is 6%, how much money should Meghan set aside today for the purchase?

Ex. 62

(a) What is the present value of $90,000 due 7 years from now, discounted at 9%?

(b) What is the present value of $150,000 due 5 years from now, discounted at 12%?

Ex. 63

Kim Kardashian plans to buy a truck for $24,000 after 3 years. If the interest rate is 6%, how much money should Kim set aside today for the purchase?

Ex. 64

Ace Manufacturing Company leases a building for 20 years. The lease requires 20 annual payments of $12,000 each, with the first payment due immediately. The interest rate in the lease is 10%. What is the present value of the cost of leasing the building?

Ex. 65

Acme Discount Retail Company is considering investing in an annuity contract that will return $50,000 annually at the end of each year for 20 years. What amount should Acme pay for this investment if it earns an 8% return?

Ex. 66

Katy Perry purchased an investment for $40,260.48. From this investment, she will receive $6,000 annually for the next 10 years starting one year from now. What rate of interest will Katy be earning on her investment?

Ex. 67

You are purchasing a car for $25,000, and you obtain financing as follows: $2,500 down payment, 12% interest, semiannual payments over 5 years.

Instructions

Compute the payment you will make every 6 months.

Ex. 68

A1 Marine Supply Company is considering investing in an annuity contract that will return $50,000 annually at the end of each year for 20 years. What amount should A1 pay for this investment if it earns an 8% return?

Ex. 69

Kim Kardashian purchased an investment for $49,090.75. From this investment, she will receive $5,000 annually for the next 20 years starting one year from now. What rate of interest will Kim be earning on her investment?

Ex. 70

Britney has just won the lottery and will receive an annual payment of $100,000 every year for the next 20 years. If the annual interest rate is 8%, what is the present value of the winnings?

Ex. 71

Suppose that CVS leases a building for 20 years. The lease requires 20 annual payments of $10,000 each, with the first payment due immediately. The interest rate in the lease is 10%. What is the present value of the cost of leasing the building?

Ex. 72

On January 2, 2025, A1 Corporation issues $6,000,000 (par value) 8%, 10-year bonds. The bonds pay interest annually on January 1. The current market rate on bonds with similar risk characteristics is 10%. What is the selling price of the bonds?

Ex. 73

Acme Auto Repair Company owns a garage and is contemplating purchasing a tire retreading machine. Acme projects a net cash inflow from the retreading machine of $10,000 annually for 7 years. It feels it could sell the machine for $8,000 when done using it. Acme hopes to earn a return of 10% on such investments. Should Acme purchase the retreading machine if it costs $50,000?

Ex. 74

To buy a house, Ryan Seacrest has signed a mortgage note to pay the American National Bank and Trust Co. with a payment of $9,000 every 6 months for 20 years. On the date the mortgage is signed, the purchase price was $230,000 and Ryan made a down payment of $20,000. The first

payment will be made 6 months after the date the mortgage is signed. Using Excel or a financial calculator, compute the exact rate of interest earned on the mortgage by the bank.