1. In order to compare different investment opportunities (each with the same risk) with interest rates reported in different manners you should

A. convert each interest rate to an annual nominal rate

B. convert each interest rate to a monthly nominal rate

C. convert each interest rate to an effective annual rate

D. compare them by using the published annual rates

E. convert each interest rate to an APR

2. Which of the following is a true statement?

A. When comparing investments it is best not to rely solely on quoted rates

B. Compounding will typically not lead to differences between the quoted rate and the effective rate

C. The APR on a loan requiring monthly payments is the interest rate you actually pay

D. An APR is the interest rate per period divided by the number of periods per year

E. With monthly compounding, the APR will be larger than the effective annual rate

3. You are examining two perpetuities which are identical in every way, except that perpetuity A will begin making annual payments of $P to you two years from today while the first $P payment of perpetuity B will occur one year from today. It must be true that

A. the present value of perpetuity A is greater than that of B by $P

B. the present value of perpetuity B is greater than that of A by $P

C. the present value of perpetuity B is equal to that of perpetuity A

D. the present value of perpetuity A exceeds that of B by the PV of $P for one year

E. the present value of perpetuity B exceeds that of A by the PV of $P for one year

4. You hold a winning ticket from your state lottery. It entitles the bearer to receive payments of $50,000 at the end of each of the next 20 years. Given what you know about the time value of money, you should be able to sell this ticket for no less than $1 million in the open market.

A. True

B. False

5. Which of the following describes the equation for finding the annuity present value factor?

A. (1 minus present value factor) times the interest rate

B. (1 plus present value factor) divided by the interest rate

C. (1 plus present value factor) times the interest rate

D. (1 minus present value factor) divided by the interest rate

E. (present value factor minus 1) divided by the interest rate

6. Which of the following describes the equation for finding the annuity future value factor?

A. (future value factor minus 1) times the interest rate

B. (future value factor plus 1) divided by the interest rate

C. (future value factor plus 1) times the interest rate

D. (future value factor minus 1) divided by the interest rate

E. (1 minus present value factor) divided by the interest rate

7. Which of the following is NOT possible to compute?

A. present value of a perpetuity

B. interest rate on a perpetuity given the present value and payment

C. present value of an annuity due

D. future value of an annuity due

E. future value of a perpetuity

8. You have $500 that you would like to invest. You have 2 choices: Savings Account A which earns 8% compounded annually or Savings Account B which earns 7.75% compounded semiannually. Which would you choose and why?

A. A because it has a higher effective annual rate

B. A because the future value in one year is lower

C. B because it has a higher effective annual rate

D. B because the future value in one year is lower

E. B because it has the higher quoted rate

9. You have $500 that you would like to invest. You have 2 choices: Savings Account A which earns 8% compounded annually or Savings Account B which earns 7.75% compounded monthly. Which would you choose and why?

A. A because it has a higher effective annual rate

B. A because the future value in one year is lower

C. B because it has a higher effective annual rate

D. B because the future value in one year is lower

E. A because it has the higher quoted rate

10. You need to borrow $18,000 to buy a truck. The current loan rate is 9.9% compounded monthly and you want to pay the loan off in equal monthly payments over 5 years. What is your monthly payment?

A. $363.39

B. $374.04

C. $381.56

D. $394.69

E. $455.66

11. Your monthly mortgage payment on your house is $593.90. It is a 30 year mortgage at 7.8% compounded monthly. How much did you borrow?

A. $75,000

B. $77,500

C. $80,000

D. $82,500

E. $85,000

12. You have just won the lottery. You and your heirs will receive $25,000 per year forever, beginning one year from now. What is the present value of this lottery given an 8% discount rate?

A. $182,500

B. $200,000

C. $287,500

D. $312,500

E. $337,500

13. You have just won the lottery. You and your heirs will receive $25,000 per year forever, beginning one year from now. If the present value of the lottery is $416,667, what is the discount rate used to value this perpetuity?

A. 4.0%

B. 5.0%

C. 6.0%

D. 7.0%

E. 8.0%

14. You have just won the lottery. You and your heirs will receive $25,000 per year forever, with the first payment due immediately. What is the present value of this lottery given an 8% discount rate?

A. $182,500

B. $200,000

C. $287,500

D. $312,500

E. $337,500

15. What is the effective annual rate of 8% compounded quarterly?

A. 8.00%

B. 8.16%

C. 8.24%

D. 8.53%

E. 16.64%

16. What is the effective annual rate of 12% compounded semiannually?

A. 11.24%

B. 12.00%

C. 12.36%

D. 12.54%

E. 12.96%

17. What is the effective annual rate of 12% compounded monthly?

A. 11.27%

B. 12.00%

C. 12.36%

D. 12.54%

E. 12.68%

18. What is the effective annual rate of 12% compounded daily?

A. 11.27%

B. 12.00%

C. 12.68%

D. 12.75%

E. 12.89%

19. A given rate is quoted as 12% APR, but has an EAR of 12.55%. What is the rate of compounding during the year?

A. annually

B. semiannually

C. quarterly

D. monthly

E. daily

20. A given rate is quoted as 8% APR, but has an EAR of 8.33%. What is the rate of compounding during the year?

A. annually

B. semiannually

C. quarterly

D. monthly

E. daily

21. What is the future value in 10 years of $1,000 payments received at the beginning of each year for the next 10 years? Assume an interest rate of 5.625%.

A. $12,259.63

B. $12,949.23

C. $13,679.45

D. $14,495.48

E. $14,782.15

22. What is the present value of $1,000 payments received at the beginning of each year for the next 10 years? Assume an interest rate of 5.625%.

A. $7,069.13

B. $7,093.62

C. $7,492.64

D. $7,914.10

E. $8,165.12

23. Fast Eddie's Used Cars will sell you a 1986 Ford Escort for $3,000 with no money down. You agree to make weekly payments for 2 years, beginning one week after you buy the car. The stated rate on the loan is 26%. How much is each payment?

A. $32.96

B. $37.06

C. $38.19

D. $45.90

E. $69.65

24. You win the lottery and are given the option of receiving $250,000 now or an annuity of $25,000 at the end of each year for 30 years. Which of the following is correct? (Ignore taxes)

A. You cannot choose between the two without first computing future values

B. You will always choose the lump regardless of interest rates

C. You will choose the annuity payment if the interest rate is 7%

D. You will always choose the annuity

E. Comparing the future value of each will lead to a different decision than comparing present values

25. You have just won a lottery prize. You can choose to receive $750,000 today or an annual payment of $50,000 at the end of each of the next twenty years. The interest rate that makes you indifferent between the two is 2.91%, and at higher rates you should take the lump sum.

A. True

B. False

26. You are planning to save your Christmas bonuses from work and are comparing savings accounts: Account A compounds semiannually while Account B compounds monthly. If both accounts have the same effective annual rate of interest and you place only the bonuses in the account, you should

A. choose Account A because it has a higher APR

B. choose Account B because it has a higher APR

C. choose Account B because it is compounded more often

D. choose Account A because you will pay less in taxes

E. choose either since you would be indifferent between the two

27. Which of the following is NOT a true statement?

A. Present values and discount rates move in the opposite directions from one another

B. On monthly compounded loans, the EAR will exceed the APR

C. Compounding essentially means earning interest on interest

D. Future values increase with increases in interest rates

E. All else equal, the longer the term of a loan the lower will be the total interest you pay on it

28. Your banker quotes you two different loan payments on a $12,000 car loan: one calling for 36 monthly payments and the other calling for 24 monthly payments. Both loans have the same APR and EAR. He then tells you that the shorter loan is a better deal because the total payments you would make over the life of the loan would be lower. What is he ignoring?

A. That the payment would be lower on the 24 month loan

B. That the 24 month contract will actually cost you more in total payments, not less

C. The interest you could earn by saving the difference between the two loan payments

D. The fact that you must make 12 more payments on the longer term loan

E. That the APR and EAR are identical

29. You are going to withdraw $1,000 at the end of each year for the next three years from an account that pays interest at a rate of 8% compounded annually. How much must there be in the account today in order for the account to reduce to a balance of zero after the last withdrawal?

A. $793.83

B. $2,577.10

C. $2,602.29

D. $2,713.75

E. $2,775.67

30. You are going to withdraw $1,000 at the end of each year for the next three years from an account that pays interest at a rate of 8% compounded annually. The account balance will reduce to zero when the last withdrawal is made. How much money will be in the account immediately after the second withdrawal is made?

A. $925.93

B. $977.10

C. $982.29

D. $1,000.00

E. $2,000.00

31. You are going to withdraw $1,000 at the end of each year for the next three years from an account that pays interest at a rate of 8% compounded annually. The account balance will reduce to zero when the last withdrawal is made. How much interest will you earn on the account over the three year life?

A. $0.00

B. $240.00

C. $422.90

D. $576.24

E. $3,000.00

32. You are going to invest $500 at the end of each year for ten years. Given an interest rate, you can find the future value of this investment by

I. adding the cash flows together and future valuing the sum by the appropriate future value factor

II. applying the proper future value factor to each cash flow, then adding up these values

III. finding the present value of each cash flow, adding all of the present values together, then finding the future value at the end of year ten of this lump sum

IV. finding the present value of the entire payment stream

A. II only

B. III only

C. II and III only

D. I, II, and IV only

E. II, III, and IV only

33. Suppose you are evaluating two annuities. They are identical in every way, except that one is an ordinary annuity and one is an annuity due. Assuming an interest rate of 10%, which of the following is true?

A. The ordinary annuity must have a higher present value than the annuity due

B. The annuity due must have the same present value as the ordinary annuity

C. The ordinary annuity must have a lower future value than the annuity due

D. The two annuities will differ in present value by the amount of exactly one of the annuity payments

E. The annuity due will have a larger present value than the ordinary annuity by an amount equal to the present value of the last annuity payment

34. At the end of each year for the next ten years you will receive cash flows of $50. If the appropriate discount rate is 5.5%, how much would you pay for the annuity?

A. $259.82

B. $299.02

C. $338.99

D. $376.88

E. $379.16

35. Suppose you invest $10 for one year, and, at the end of the year you receive $12. Which of the following is NOT true about the rate at which you invested?

A. The quoted rate must have been greater than 20%

B. To figure the quoted rate you would need to know how often the investment was compounded

C. The EAR at which you invested was certainly 20%

D. The daily compounded effective annual rate would certainly have been 20%

E. The EAR would be the same whether compounding quarterly or semiannually

36. At the end of each year for the next ten years you will receive cash flows of $50. The initial investment is $320. What rate of return are you expecting from this investment?

A. 9.06%

B. 10.27%

C. 12.01%

D. 12.28%

E. 13.21%

37. You are considering investing $750 in a 10 year annuity. The rate of return you feel you require is 6.5%. What annual cash flow from the annuity will provide the required return?

A. $ 70.77

B. $102.96

C. $104.33

D. $114.31

E. $129.27

38. You are considering an investment with a quoted return of 10% per year. If interest is compounded daily, what is the effective return on this investment?

A. 1.11%

B. 10.00%

C. 10.25%

D. 10.47%

E. 10.52%

39. You notice a local consumer finance company is offering 20% APR loans, but compounds interest daily. What is the EAR?

A. 12.21%

B. 22.13%

C. 23.61%

D. 24.97%

E. 25.83%

40. You borrowed $1,500 at 6% compounded annually. Your payments are $90 at the end of each year. How many years will you make payments on the loan?

A. 9 years

B. 10 years

C. 11 years

D. 12 years

E. forever

41. You agree to loan your parents $22,000 to buy a new van. They agree to pay you $450 a month for 5 years. The ________________.

A. interest rate on the loan is 0.75% per month

B. APR on the loan is 8.17%

C. EAR on the loan is 8.37%

D. APR on the loan is 8.68%

E. EAR on the loan is 8.7%

42. Your brother-in-law borrowed $2,000 from you 4 years ago and then disappeared. Yesterday he returned and expressed a desire to pay back the loan, including the interest accrued. Assuming that you had agreed to charge him 10% compounded annually, and assuming that he wishes to make five equal annual payments beginning in one year, how much would your brother-in-law have to pay you annually in order to extinguish the debt? (Assume that the loan continues to accrue interest at 10% per year.)

A. $697.43

B. $738.63

C. $751.46

D. $772.45

E. $798.24

43. Mr. Dubofsky just won a "Name That Tune" contest with a grand prize of $250,000. However, the contest stipulates that the winner will receive $100,000 immediately, and $15,000 at the end of each of the next 10 years. Assuming that he can earn 5% on his money, how much has he actually won?

A. $92,156.46

B. $98,225.11

C. $115,826.02

D. $215,826.02

E. $250,000.00

44. Deryl wishes to save money to provide for his retirement. Beginning one month from now, he will begin depositing a fixed amount into a retirement savings account that will earn 12% compounded monthly. He will make 360 such deposits. Then, one year after making his final deposit, he will withdraw $100,000 annually for 25 years. The fund will continue to earn 12% compounded monthly. How much should his monthly deposits be?

A. $205.28

B. $209.58

C. $214.21

D. $234.89

E. $249.38

45. You have $10,000 to invest. The First National Bank offers one-year certificates of deposit with a stated rate of 5.50% compounded quarterly. What rate compounded semiannually would provide you with the same amount of money at the end of one year?

A. 5.487%

B. 5.500%

C. 5.507%

D. 5.512%

E. 5.538%

46. Vito Corleone will loan you money on a "five-for-six" arrangement; i.e., for every $5 he gives you today, you give him $6 one week from now. What is the APR of this loan?

A. 410%

B. 540%

C. 860%

D. 1,040%

E. 1,310%

47. Vito Corleone will loan you money on a "five-for-six" arrangement; i.e., for every $5 he gives you today, you give him $6 one week from now. What is the EAR of this loan?

A. 410%

B. 540%

C. 860%

D. 1,040%

E. 13,104%

48. You own a bond issued by the Canadian Pacific railroad which promises to pay the holder $100 annually forever. You plan to sell the bond five years from now. If similar investments yield 8% at that time, how much will the bond be worth?

A. $918.79

B. $1,014.28

C. $1,250.00

D. $1,489.42

E. $1,958.20

49. Moe purchases a $100, 30-year annuity. Larry purchases a $100 perpetuity. In both cases, payments begin in one year, and the appropriate interest rate is 10%. What is the present value today of Larry's payments occurring from year 31 on?

A. $51.15

B. $57.31

C. $58.11

D. $81.21

E. More than $100

50. Moe purchases a $100 perpetuity on which payments begin in one year. Larry purchases a $100 perpetuity on which payments begin immediately. Both make annual payments and a 10% interest rate is appropriate for both cash flow streams. Which of the following statements is true?

A. Moe's perpetuity is worth $100 more than Larry's

B. Larry's perpetuity is worth $100 more than Moe's

C. The perpetuities are of equal value today

D. Larry's perpetuity is worth $90.91 more than Moe's

E. Moe's perpetuity is worth $90.91 more than Larry's

51. In order to help you through college, your parents just deposited $25,000 into a bank account paying 8% interest. Starting tomorrow, you plan to withdraw equal amounts from the account at the beginning of each of the next four years. What is the MOST you can withdraw annually?

A. $ 6,125.43

B. $ 6,988.91

C. $ 7,133.84

D. $ 7,548.02

E. $ 8,154.71

52. In order to help you through college, your parents just deposited $25,000 into a bank account paying 8% interest. Starting next year, you plan to withdraw equal amounts from the account at the end of each of the next four years. What is the MOST you can withdraw annually?

A. $ 6,125.43

B. $ 6,988.91

C. $ 7,133.84

D. $ 7,548.02

E. $ 8,154.71

53. Analysts expect Marble Comics to pay shareholders $1.00 per share annually for the next five years. After that, the dividend will be $1.50 annually forever. Given a discount rate of 10%, what is the value of the stock today?

A. $6.55

B. $9.87

C. $12.37

D. $13.10

E. $21.88

54. The preferred stock of Marble Comics currently sells for $31.25 per share. The annual dividend of $2.50 is fixed. Assuming a constant dividend forever, what is the rate of return on this stock?

A. 4.5%

B. 6.0%

C. 8.0%

D. 9.5%

E. 12.5%

55. Fast Eddie's Used Cars will sell you a 1986 Ford Escort for $3,000 with no money down. You agree to make weekly payments of $40.00 for 2 years, beginning one week after you buy the car. What is the EAR of this loan?

A. 34.43%

B. 36.55%

C. 40.94%

D. 42.34%

E. 53.01%

56. What is the present value of $1,000 payments received at the beginning of each year for the next 10 years? Assume an interest rate of 5.49% compounded monthly.

A. $7,069.13

B. $7,093.62

C. $7,492.64

D. $7,912.58

E. $7,955.26

57. Five years from now you will begin to receive cash flows of $75 per year. These cash flows will continue forever. If the discount rate is 6%, what is the present value of these cash flows?

A. $799.68

B. $894.22

C. $934.07

D. $990.12

E. $1,104.67

58. Four years from now you will receive the first of seven annual $10,000 payments. The current interest rate is 6%, but by the beginning of year 4, the rate will have risen to 8%. What is the present value of this cash flow stream?

A. $41,827.45

B. $42,554.49

C. $43,713.69

D. $46,864.49

E. $55,692.45

59. What rate of return compounded daily allows you to triple your money in 20 years?

A. 5.49%

B. 5.98%

C. 6.86%

D. 6.92%

E. 8.99%

60. Your local bank just loaned you $1,500. This amount is net of a 10% discount on the loan proceeds, which serves as interest on the loan. You are to repay the loan in one year. What is the effective rate at which you borrowed?

A. 11.00%

B. 11.11%

C. 11.97%

D. 12.58%

E. 12.64%

61. Your local S&L provides you with the following information concerning a possible single payment loan. You pay 2 "points" (1 point=1%) up front, and the interest rate you are charged is 10%. If you borrow $4,000 for one year on these terms, at what rate are you actually borrowing? (Hint: deduct the points from the loan proceeds.)

A. 10.59%

B. 11.04%

C. 11.20%

D. 12.24%

E. 12.48%

62. The company you work for will deposit $600 at the end of each month into your retirement fund. Interest is compounded monthly. You plan to retire 15 years from now and estimate that you will need $2,000 per month out of the account for the next 20 years. If the account pays 8.0% compounded monthly, how much do you need to put into the account in addition to your company deposit in order to meet your objective?

A. $0.00

B. $57.59

C. $90.99

D. $95.88

E. $104.49

63. You work for a furniture store. You normally sell a living room set for $2,500 and finance the full purchase price for 30 monthly payments at 24% APR. You are planning to

run a zero-interest financing sale during which you will finance the set over 30 months at 0% interest. How much do you need to charge for the bedroom set during the sale in order to earn your usual combined return on the sale and the financing?

A. $2,500

B. $2,827

C. $3,348

D. $3,437

E. $3,784

64. You work for a furniture store. You normally sell a living room set for $2,500 and finance the full purchase price for 30 monthly payments at 24% APR. You are planning to run a zero-interest financing sale during which you will finance the set over 30 months at 0% interest. How much do you need to raise the price of the bedroom set during the sale in order to earn your usual combined return on the sale and the financing?

A. $0

B. $848

C. $892

D. $937

E. $1,284

65. You work for a furniture store. You normally sell a living room set for $2,500 and finance the full purchase price for 30 monthly payments at 24% APR. You are planning to run a zero-interest financing sale during which you will finance the set over 30 months at 0% interest. What is the monthly payment on a zero-interest loan that you must charge during the sale in order to earn your usual combined return on the sale and the financing?

A. $83.33

B. $89.72

C. $95.24

D. $111.62

E. $128.43

66. You are planning to borrow $2,500. You can repay the loan in 40 monthly payments of $79.06 each or 36 monthly payments of $85.93 each. You decide to take the 40 month loan. During each of the first 36 months you make the loan payment and place the difference between the two payments ($6.87) into a savings account earning 14.4% APR. Beginning with the 37th payment you will withdraw money from the savings account to make your payments. How much money will remain in the savings account after your loan is repaid?

A. -$5.00

B. $0.00

C. $3.25

D. $19.78

E. $495.50

67. You deposit $1,000 in an account today. You will deposit $600 at the end of each month for the next 12 months and $800 the following 12 months. How much interest will you have earned in 2 years if the account pays 5.5% compounded monthly?

A. $795.42

B. $827.65

C. $849.42

D. $962.57

E. $979.00

68. You have $1,225 in a savings account which earns 8.4% compounded monthly and $1,300 in an account which earns 6% compounded monthly. How many years will it be until the two accounts have the same amount in them if you do not withdraw any money?

A. 1.54 years

B. 1.97 years

C. 2.39 years

D. 2.50 years

E. 2.69 years

69. If you deposit $2,500 at the end of each six months into an account which earns 5.5% interest compounded quarterly, how much will be in the account in 5 years?

A. $13,953

B. $16,931

C. $26,605

D. $28,357

E. $32,188

70. What would your payment be on a 10-year, $150,000 loan at 10% compounded semi-annually assuming payments are made annually?

A. $19,716.67

B. $20,743.77

C. $24,411.81

D. $24,674.60

E. $25,366.63

71. When you were born, your dear old Aunt Minnie promised to deposit $1,000 into a savings account bearing a 5% annually compounded rate on each birthday, beginning with your first. You have just turned 22 and want the dough, However, it turns out that dear old (forgetful) aunt Minnie made no deposits on your fifth and eleventh birthdays. How much is in the account right now?

A. $31,976

B. $34,503

C. $43,888

D. $47,983

E. $51,889

72.

You and your spouse have found your dream home in Rapid City, South Dakota. The selling price is $120,000; you will put $20,000 down and obtain a 30-year fixed-rate mortgage at 8.25% for the rest.

R-1 5-1

Assume that monthly payments begin in one month. What will each payment be?

A. $725.01

B. $751.27

C. $757.76

D. $825.45

E. $901.52

73.

You and your spouse have found your dream home in Rapid City, South Dakota. The selling price is $120,000; you will put $20,000 down and obtain a 30-year fixed-rate mortgage at 8.25% for the rest.

R-1 5-1

How much interest will you pay (in dollars) over the life of the loan? (Assume you make each of the required 360 payments on time.)

A. $135,101

B. $145,583

C. $170,457

D. $190,457

E. $270,457

74.

You and your spouse have found your dream home in Rapid City, South Dakota. The selling price is $120,000; you will put $20,000 down and obtain a 30-year fixed-rate mortgage at 8.25% for the rest.

R-1 5-1

Although you will get a 30-year mortgage, you plan to prepay the loan by making an additional payment each month along with your regular payment. How much extra must you pay each month if you wish to pay off the loan in 20 years?

A. $24.56

B. $54.88

C. $100.80

D. $103.28

E. $106.86

75.

You and your spouse have found your dream home in Rapid City, South Dakota. The selling price is $120,000; you will put $20,000 down and obtain a 30-year fixed-rate mortgage at 8.25% for the rest.

R-1 5-1

Your banker suggests that, rather than obtaining a 30-year mortgage and paying it off early, you should simply obtain a 15-year loan for the same amount. The rate on this loan is 7.75%. By how much will your monthly payment be (higher/lower) for the 15-year loan than the regular payment on the 30-year loan?

A. lower; $111.57

B. lower; $54.72

C. higher; $9.26

D. higher; $190.01

E. higher; $194.59

76.

Rob and Laura wish to buy a new home. The price is $187,500 and they plan to put 20% down. New Rochelle Savings and Loan will lend them the remainder at a 10% fixed rate for 30 years, with monthly payments to begin in one month. (Ignore taxes.)

R-2 5-2

How much will their monthly payments be?

A. $1,316.36

B. $1,325.99

C. $1,512.56

D. $1,645.45

E. $1,760.45

77.

Rob and Laura wish to buy a new home. The price is $187,500 and they plan to put 20% down. New Rochelle Savings and Loan will lend them the remainder at a 10% fixed rate for 30 years, with monthly payments to begin in one month. (Ignore taxes.)

R-2 5-2

Assuming they pay off the loan over the 30 year period as planned, what will the total cost (principal + interest + down payment) of the house be?

A. $187,500

B. $271,996

C. $354,234

D. $473,760

E. $511,390

78.

Rob and Laura wish to buy a new home. The price is $187,500 and they plan to put 20% down. New Rochelle Savings and Loan will lend them the remainder at a 10% fixed rate for 30 years, with monthly payments to begin in one month. (Ignore taxes.)

R-2 5-2

What will the outstanding balance of the loan be after ten years assuming they make the first 120 payments right on time?

A. $99,610

B. $135,467

C. $136,407

D. $139,144

E. $170,509

79.

Rob and Laura wish to buy a new home. The price is $187,500 and they plan to put 20% down. New Rochelle Savings and Loan will lend them the remainder at a 10% fixed rate for 30 years, with monthly payments to begin in one month. (Ignore taxes.)

R-2 5-2

Suppose Rob wants to pay off the loan in 15 years. How much extra must he pay each month to do so?

A. $11.25

B. $201.99

C. $295.55

D. $311.55

E. $314.47

80.

Rob and Laura wish to buy a new home. The price is $187,500 and they plan to put 20% down. New Rochelle Savings and Loan will lend them the remainder at a 10% fixed rate for 30 years, with monthly payments to begin in one month. (Ignore taxes.)

R-2 5-2

Assume that, in order to receive the 30-year loan from Brady Financing, Rob and Laura must pay 3 "points" at the time the loan is originated. (One point equals 1% of the amount to be borrowed.) What is the effective interest rate (EAR) on this loan, after taking the points into account? (Hint: find the discount rate that equates the loan amount with the present value of the loan payments plus the points paid.)

A. 9.11%

B. 10.00%

C. 10.37%

D. 10.47%

E. 10.87%

81.

Given the recent drop in mortgage interest rates, you have decided to refinance your home. Exactly five years ago, you obtained a $100,000 30-year mortgage with a fixed rate of 10%. Today you can get a 30-year loan for the currently outstanding balance at 8%. This loan, however, requires you to pay a $250 appraisal fee and 3 points at the time of the refinancing. (Hints: (a) 1 point equals 1% of the amount borrowed, and (b) ignore tax considerations.)

R-3 5-3

What is the outstanding balance on the loan today, if you just made the 60th payment?

A. $88,144

B. $90,938

C. $96,574

D. $98,159

E. $105,159

82.

Given the recent drop in mortgage interest rates, you have decided to refinance your home. Exactly five years ago, you obtained a $100,000 30-year mortgage with a fixed rate of 10%. Today you can get a 30-year loan for the currently outstanding balance at 8%. This loan, however, requires you to pay a $250 appraisal fee and 3 points at the time of the refinancing. (Hints: (a) 1 point equals 1% of the amount borrowed, and (b) ignore tax considerations.)

R-3 5-3

How much will your monthly payments be after you refinance?

A. $443.96

B. $505.67

C. $652.90

D. $708.63

E. $733.76

83.

Given the recent drop in mortgage interest rates, you have decided to refinance your home. Exactly five years ago, you obtained a $100,000 30-year mortgage with a fixed rate of 10%. Today you can get a 30-year loan for the currently outstanding balance at 8%. This loan, however, requires you to pay a $250 appraisal fee and 3 points at the time of the refinancing. (Hints: (a) 1 point equals 1% of the amount borrowed, and (b) ignore tax considerations.)

R-3 5-3

By how much will your monthly payments drop if you refinance?

A. $111.98

B. $139.36

C. $143.81

D. $161.82

E. $168.94

84.

Given the recent drop in mortgage interest rates, you have decided to refinance your home. Exactly five years ago, you obtained a $100,000 30-year mortgage with a fixed rate of 10%. Today you can get a 30-year loan for the currently outstanding balance at 8%. This loan, however, requires you to pay a $250 appraisal fee and 3 points at the time of the refinancing. (Hints: (a) 1 point equals 1% of the amount borrowed, and (b) ignore tax considerations.)

R-3 5-3

How much is the up-front cash outlay required for you to obtain refinancing?

A. $2,897.22

B. $3,058.52

C. $3,147.22

D. $3,187.53

E. $3,250.00

85.

Given the recent drop in mortgage interest rates, you have decided to refinance your home. Exactly five years ago, you obtained a $100,000 30-year mortgage with a fixed rate of 10%. Today you can get a 30-year loan for the currently outstanding balance at 8%. This loan, however, requires you to pay a $250 appraisal fee and 3 points at the time of the refinancing. (Hints: (a) 1 point equals 1% of the amount borrowed, and (b) ignore tax considerations.)

R-3 5-3

Ignoring time value considerations, how many months must you stay in the house to make the refinancing worthwhile? (In other words, how many months are required for the payment savings to equal the dollar outlays required to refinance?)

A. 13 months

B. 16 months

C. 17 months

D. 18 months

E. 19 months

86.

Given the recent drop in mortgage interest rates, you have decided to refinance your home. Exactly five years ago, you obtained a $100,000 30-year mortgage with a fixed rate of 10%. Today you can get a 30-year loan for the currently outstanding balance at 8%. This loan, however, requires you to pay a $250 appraisal fee and 3 points at the time of the refinancing. (Hints: (a) 1 point equals 1% of the amount borrowed, and (b) ignore tax considerations.)

R-3 5-3

At the refinancing rate of 8%, how many months must you stay in the house to make the refinancing worthwhile? (In other words, how many months are required for the payment savings to equal the dollar outlays required to refinance?)

A. 17 months

B. 18 months

C. 19 months

D. 20 months

E. 21 months

87.

Given the recent drop in mortgage interest rates, you have decided to refinance your home. Exactly five years ago, you obtained a $100,000 30-year mortgage with a fixed rate of 10%. Today you can get a 30-year loan for the currently outstanding balance at 8%. This loan, however, requires you to pay a $250 appraisal fee and 3 points at the time of the refinancing. (Hints: (a) 1 point equals 1% of the amount borrowed, and (b) ignore tax considerations.)

R-3 5-3

For the drop in monthly payments under the refinancing, how much is attributable to the lower interest rate, as opposed to the amount that is attributable to extending the remaining maturity of your mortgage from 25 years to 30 years?

A. $117.11

B. $126.75

C. $132.20

D. $140.80

E. $168.94

88.

With auto loans extending 5,6,7 or more years these days, it is common for buyers who wish to trade their cars in after a few years to find themselves to be "upside down". In other words, the outstanding principal on the auto loan exceeds the value of the car being traded. Suppose you buy a new Toyota for $20,000, paying nothing down. You agree to a repayment schedule of 6 equal annual payments beginning one year from today. The banker's required return is

9%, compounded annually. Assume the car will lose 20% of its value the first year, and 10% ($2,000) each year thereafter.

R-4 5-4

How much will your annual payments be?

A. $3,729.03

B. $4,458.40

C. $5,121.24

D. $6,664.91

E. $7,563.01

89.

With auto loans extending 5,6,7 or more years these days, it is common for buyers who wish to trade their cars in after a few years to find themselves to be "upside down". In other words, the outstanding principal on the auto loan exceeds the value of the car being traded. Suppose you buy a new Toyota for $20,000, paying nothing down. You agree to a repayment schedule of 6 equal annual payments beginning one year from today. The banker's required return is 9%, compounded annually. Assume the car will lose 20% of its value the first year, and 10% ($2,000) each year thereafter.

R-4 5-4

Given the depreciation schedule above, how much will the car be worth after 3 years?

A. $10,000

B. $12,000

C. $14,000

D. $16,000

E. $20,000

90.

With auto loans extending 5,6,7 or more years these days, it is common for buyers who wish to trade their cars in after a few years to find themselves to be "upside down". In other words, the outstanding principal on the auto loan exceeds the value of the car being traded. Suppose you buy a new Toyota for $20,000, paying nothing down. You agree to a repayment schedule of 6 equal annual payments beginning one year from today. The banker's required return is 9%, compounded annually. Assume the car will lose 20% of its value the first year, and 10% ($2,000) each year thereafter.

R-4 5-4

Given the depreciation schedule above, how much will the car be worth after you have made your final payment?

A. $4,000

B. $6,000

C. $8,000

D. $10,000

E. $12,000

91.

With auto loans extending 5,6,7 or more years these days, it is common for buyers who wish to trade their cars in after a few years to find themselves to be "upside down". In other words, the outstanding principal on the auto loan exceeds the value of the car being traded. Suppose you buy a new Toyota for $20,000, paying nothing down. You agree to a repayment schedule of 6 equal annual payments beginning one year from today. The banker's required return is 9%, compounded annually. Assume the car will lose 20% of its value the first year, and 10% ($2,000) each year thereafter.

R-4 5-4

Including principal and interest, what is your total cost for this car? (Assume you make all of your payments on time.)

A. $20,000

B. $24,999

C. $26,750

D. $27,899

E. $31,872

92.

With auto loans extending 5,6,7 or more years these days, it is common for buyers who wish to trade their cars in after a few years to find themselves to be "upside down". In other words, the outstanding principal on the auto loan exceeds the value of the car being traded. Suppose you buy a new Toyota for $20,000, paying nothing down. You agree to a repayment schedule of 6 equal annual payments beginning one year from today. The banker's required return is 9%, compounded annually. Assume the car will lose 20% of its value the first year, and 10% ($2,000) each year thereafter.

R-4 5-4

After which loan payment will you be "right-side up" for the first time? (At what point does the market value of the car exceed the outstanding balance of the loan for the first time?)

A. After payment number 1

B. After payment number 2

C. After payment number 3

D. After payment number 4

E. After payment number 5

93.

With auto loans extending 5,6,7 or more years these days, it is common for buyers who wish to trade their cars in after a few years to find themselves to be "upside down". In other words, the outstanding principal on the auto loan exceeds the value of the car being traded. Suppose you buy a new Toyota for $20,000, paying nothing down. You agree to a repayment schedule of 6 equal annual payments beginning one year from today. The banker's required return is

9%, compounded annually. Assume the car will lose 20% of its value the first year, and 10% ($2,000) each year thereafter.

R-4 5-4

Assume the information as given above, except that you put $2,000 down on the car, so that you only had to borrow $18,000. Now, after which loan payment will you be "right-side up" for the first time?

A. After payment number 1

B. After payment number 2

C. After payment number 3

D. After payment number 4

E. After payment number 5

94. Using the example of a savings account, explain the difference between the EAR and the APR.

Answer:

95. If you ran a bank, which rate would you rather advertise on monthly-compounded loans, the EAR or the APR? Which rate would you rather advertise on quarterly-compounded savings accounts, the EAR or the APR? Explain. As a consumer of the bank's products, which would you prefer to see and why?

Answer:

96. You are considering two annuities, both of which make total annuity payments of $10,000 over their life. Which would be worth more today, annuity A which pays $1,000 at

the end of each year for the next 10 years, or annuity B which pays $775 at the end of the first year, but the annuity payment grows by $50 each year, reaching $1,225 at the end of the 10th year? Are there any circumstances in which the two would be equal? Explain your reasoning.

Answer:

97. There are three factors that affect the present value of an annuity. Explain what these three factors are and discuss how an increase in each will impact the present value of the annuity.

Answer:

98. There are three factors that affect the future value of an annuity. Explain what these three factors are and discuss how an increase in each will impact the future value of the annuity.

Answer:

99. Should lending laws be changed to require lenders to report the EAR rather than the APR? Explain.

Answer:

100. Annuity A makes annual payments of $813.73 for each of the next 10 years, while annuity B makes annual payments of $500 per year forever. At what interest rate would you be indifferent between the two? At interest rates above this break-even rate, which annuity would you choose? How about below?

Answer:

101. Write out the formula for the present value of an annuity. Then, multiply both sides by (1 + R)*Pt . Interpret the result you see on both the left side and right sides of the equal sign. (Note that with a little manipulation, the right-hand side should look like another one of the annuity formulas.) What does this suggest to you about finding the future value of an annuity?

Answer:

102. A friend who owns an annuity that promises to pay $1,000 at the end of each year, forever, comes to you and offers to sell you all of the payments to be received after the 25th year for the value of $1,000 or one annuity payment. At an interest rate of 10%, should you pay $1,000 today to receive payment numbers 26 on to infinity? What does this suggest to you about the value of the perpetual payments?

Answer:

103. You need a business loan, and your local bank offers you two options. The first calls for fixed annual payments over five years with a fixed interest rate of 8%. The second calls for a variable interest rate of 2% over prime, which equates to a rate of 8% today. The second loan also requires annual payments, with the payment adjusted each year so that the loan amortizes to zero with the last payment, the same as it does for the fixed rate loan. There is no prepayment penalty, so you can pay the loan off at any time. Which would you take and why? Explain the result of your choice if interest rates rise and if interest rates fall.