The questions marked with symbol have not been graded.Responses to questions are indicated by the symbol.

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 rateB. convert each interest rate to a monthly nominal rateC. convert each interest rate to an effective annual rateD. compare them by using the published annual ratesE. 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 ratesB. Compounding will typically not lead to differences between the quoted rate and

the effective rateC. The APR on a loan requiring monthly payments is the interest rate you actually

payD. An APR is the interest rate per period divided by the number of periods per yearE. 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 $PB. the present value of perpetuity B is greater than that of A by $PC. the present value of perpetuity B is equal to that of perpetuity AD. the present value of perpetuity A exceeds that of B by the PV of $P for one yearE. 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. TrueB. 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 rateB. (1 plus present value factor) divided by the interest rateC. (1 plus present value factor) times the interest rateD. (1 minus present value factor) divided by the interest rateE. (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 rateB. (future value factor plus 1) divided by the interest rateC. (future value factor plus 1) times the interest rateD. (future value factor minus 1) divided by the interest rateE. (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 perpetuityB. interest rate on a perpetuity given the present value and paymentC. present value of an annuity dueD. future value of an annuity dueE. 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 rateB. A because the future value in one year is lowerC. B because it has a higher effective annual rateD. B because the future value in one year is lowerE. 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 rateB. A because the future value in one year is lowerC. B because it has a higher effective annual rateD. B because the future value in one year is lowerE. 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. $363.39B. $374.04C. $381.56D. $394.69E. $455.66

18,000 = C*[(1 - 1/{(1 + .099/12)^60)}/(.099/12)]; C = $381.56

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. $75,000B. $77,500C. $80,000D. $82,500E. $85,000

PV = 593.90*[(1 - 1/{(1 + .078/12)^360)}/(.078/12)]; PV = $82,500

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. $200,000C. $287,500D. $312,500E. $337,500

PV = 25,000/.08 = $312,500

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%

I = 25000/416667 = 6%

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. $182,500B. $200,000C. $287,500D. $312,500E. $337,500

PV = 25,000/.08 + 25,000 = $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%

EAR = (1 + .08/4)^4 - 1 = 8.24%

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%

EAR = (1 + .12/2)^2 - 1 = 12.36%

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%

EAR = (1 + .12/12)^12 - 1 = 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%

EAR = (1 + .12/365)^365 - 1 = 12.75%

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. annuallyB. semiannuallyC. quarterlyD. monthlyE. daily

.1255 = (1 + .12/m)^m - 1; m = 4

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. annuallyB. semiannuallyC. quarterlyD. monthlyE. daily

0.833 = (1 + .08/m)^m - 1; m = 365 (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. $12,259.63B. $12,949.23C. $13,679.45D. $14,495.48E. $14,782.15

FV = 1000*[{(1 + .05625)^10 - 1}/.05625]*(1 + .05625) = $13,679.45

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. $7,069.13B. $7,093.62C. $7,492.64D. $7,914.10E. $8,165.12

PV = 1000*[(1 - 1/{(1 + .05625)^10)}/(.05625)]*(1 + .05625) = $7,914.10

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. $32.96B. $37.06C. $38.19D. $45.90E. $69.65

PV = 3,000 = C*[(1 - 1/{(1 + .26/52)^104)}/(.26/52)]; C = $37.06

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 valuesB. You will always choose the lump regardless of interest ratesC. You will choose the annuity payment if the interest rate is 7%D. You will always choose the annuityE. 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. TrueB. 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 APRB. choose Account B because it has a higher APRC. choose Account B because it is compounded more oftenD. choose Account A because you will pay less in taxesE. 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

anotherB. On monthly compounded loans, the EAR will exceed the APRC. Compounding essentially means earning interest on interestD. Future values increase with increases in interest ratesE. 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 loanB. That the 24 month contract will actually cost you more in total payments, not

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

paymentsD. The fact that you must make 12 more payments on the longer term loanE. 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. $793.83B. $2,577.10C. $2,602.29D. $2,713.75E. $2,775.67

PV = 1000*[(1 - 1/{(1 + .08)^3)}/(.08)] = $2,577.10

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. $925.93B. $977.10C. $982.29D. $1,000.00E. $2,000.00

PV = 1000/1.08 = $925.93

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. $0.00B. $240.00C. $422.90D. $576.24E. $3,000.00

PV = 1000*[(1 - 1/{(1 + .08)^3)}/(.08)] = $2,577.10; int. = 3,000 - 2,577.10 = $422.90

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 byI. adding the cash flows together and future valuing the sum by the appropriate future value factorII. applying the proper future value factor to each cash flow, then adding up these valuesIII. 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 sumIV. finding the present value of the entire payment stream

A. II onlyB. III onlyC. II and III onlyD. I, II, and IV onlyE. II, III, and IV only

PV = 50*[(1 - 1/{(1 + .055)^10)}/(.055)] = $376.88

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 dueB. The annuity due must have the same present value as the ordinary annuityC. The ordinary annuity must have a lower future value than the annuity dueD. The two annuities will differ in present value by the amount of exactly one of

the annuity paymentsE. 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. $259.82B. $299.02C. $338.99D. $376.88E. $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 compoundedC. 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%

320 = 50*[(1 - 1/{(1 + r)^10)}/(r)] = 9.06%

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. $ 70.77B. $102.96C. $104.33D. $114.31E. $129.27

PV = 750 = C*[(1 - 1/{(1 + .065)^10)}/(.065)]; C = $104.33

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%

EAR = (1 + .1/365)^365 - 1 = 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%

EAR = (1 + .2/365)^365 - 1 = 22.13%

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 yearsB. 10 yearsC. 11 yearsD. 12 yearsE. forever

Annual interest = $1500*.06 = $90; principal never declines

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 monthB. 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%

22,000 = 450*[(1 - 1/{(1 + r)^60)}/(r)]; APR = 8.37%; EAR = (1 + .0837/12)^12 - 1 = 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. $697.43B. $738.63C. $751.46D. $772.45E. $798.24

Loan balance = 2000*(1 + .1)^4 = $2,928.20; 2,928.20 = C*[(1 - 1/{(1 + .1)^5)}/(.1)]; C = $772.45

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. $92,156.46B. $98,225.11C. $115,826.02D. $215,826.02E. $250,000.00

PV = 15,000*[(1 - 1/{(1 + .05)^10)}/(.05)] = 115,826.02 + 100,000 = $215,826.02

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. $205.28B. $209.58C. $214.21D. $234.89E. $249.38

EAR = (1 + .01)^12 = 12.6825%; PV retirement = 100,000*[(1 - 1/{(1 + .126825)^25)}/(.126825) = $748,642.21 FV = 748,642.21 = C*[{(1 + .01)^360 - 1}/.01]; C = $214.21

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%

EAR = (1 + .055/4)^4 - 1 = 5.614%; APR = .05614 = (1 + q/2)^2 - 1; q = 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%

Rate per period = 6/5 - 1 = 20%; APR = 20%*52 = 1,040%

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%

Rate per period = 6/5 - 1 = 20%; EAR = (1 + .2)^52 - 1 = 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. $918.79B. $1,014.28C. $1,250.00D. $1,489.42E. $1,958.20

PV = 100/.08 = $1,250 always

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. $57.31C. $58.11D. $81.21E. More than $100

PV perp = 100/.1 = $1,000; PV annuity = 100*[(1 - 1/{(1 + .1)^30)}/(.01)] = $942.69; PV difference = 1,000 - 942.69 = $57.31

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'sB. Larry's perpetuity is worth $100 more than Moe'sC. The perpetuities are of equal value todayD. Larry's perpetuity is worth $90.91 more than Moe'sE. 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. $ 6,125.43B. $ 6,988.91C. $ 7,133.84D. $ 7,548.02E. $ 8,154.71

PV = 25,000 = C*[(1 - 1/{(1 + .08)^4)}/(.08)]; C = 7,548.02/(1.08) = $6,988.91

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. $ 6,125.43B. $ 6,988.91

C. $ 7,133.84D. $ 7,548.02E. $ 8,154.71

PV = 25,000 = C*[(1 - 1/{(1 + .08)^4)}/(.08)]; C = $7,548.02

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. $6.55B. $9.87C. $12.37D. $13.10E. $21.88

PV years 6 on = 1.50/.1 = $15, PV today = 15/(1.1)^5 = $9.31 PV annuity = 1*[(1 - 1/{(1 + .1)^5)}/(.1)] = $3.79; Total PV = 9.31 + 3.79 = $13.10

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%

Rate = 2.5/31.25 = 8%

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%

PV = 3,000 = 40*[(1 - 1/{(1 + r)^104)}/(r)]; r = 34.43% (APR) EAR = (1 + .3443/52)^52 - 1 = 40.94%

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. $7,069.13B. $7,093.62C. $7,492.64D. $7,912.58E. $7,955.26

EAR = (1 + .0549/12)^12 - 1 = 5.63%; PV = 1000*[(1 - (1/1.0563^10))/.0563]*1.0563 = $7,912.58

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. $799.68B. $894.22C. $934.07D. $990.12E. $1,104.67

PV = 75/.06 = 1,250/(1.06)^4 = $990.12

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. $41,827.45B. $42,554.49C. $43,713.69D. $46,864.49E. $55,692.45

PV = 10000*[(1 - 1/{(1 + .08)^7)}/(.08)] = $52,063.70/(1 + .06)^3 = $43,713.69

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%

3 = 1*[(1 + r/365)^365]^20; r = 5.49%

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%

Gross proceeds = 1500/.9 = 1666.67; interest = 166.67; rate = 166.67/1500 = 11.11%

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%

Proceeds = $4000*.98 = 3,920; 3920 = 4000*1.1/(1 + r); r = 12.24%

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. $0.00B. $57.59C. $90.99D. $95.88E. $104.49

Need = 2000*[(1 - 1/{(1 + .08/12)^240)}/(.08/12)] = $239,108.58 Payment = 239108.58 = C*[{(1 + .08/12)^180 - 1}/(.08/12)]; C = 690.99 You must pay 690.99 - 600 = $90.99 more

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. $2,500B. $2,827C. $3,348D. $3,437E. $3,784

25,000 = C*[(1 - 1/{(1 + .02)^30)}/(.02)]; C = $111.62; 0% price = 111.62*30 = $3,348

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. $0B. $848C. $892D. $937

E. $1,284

25,000 = C*[(1 - 1/{(1 + .02)^30)}/(.02)]; C = $111.62 0% price = 111.62*30 = $3,348; raise = 3348 - 2500 = $848

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. $83.33B. $89.72C. $95.24D. $111.62E. $128.43

25,000 = C*[(1 - 1/{(1 + .02)^30)}/(.02)]; C = $111.62

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. -$5.00B. $0.00C. $3.25D. $19.78E. $495.50

Loan balance after 36 pmts = 79.06*[(1 - 1/{(1 + .012)^4)}/(.012)]; PV = $306.97 Balance in savings after 36 months = 6.87*[(1 + .012)^36 - 1]/.012 = $307.08 Since the balances are essentially equal, the balance at the end will be about $0

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. $795.42B. $827.65C. $849.42D. $962.57E. $979.00

12 mos = 1,000*(1 + .055/12)^12 + 600*[(1 + .055/12)^12 - 1]/(.055/12) = 8,440.71 24 mos = 8,440.71*(1 + .055/12)^12 + 800*[(1 + .055/12)^12 - 1]/(.055/12) = 18,762.57 Interest earned = $18,762.57 - 1,000 - 12*600 - 12*800 = $962.57

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 yearsB. 1.97 yearsC. 2.39 yearsD. 2.50 yearsE. 2.69 years

1,225*(1 + .084/12)^n = 1,300*(1 + .06/12)^n; n = 29.88/12 = 2.5 yrs

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. $13,953B. $16,931C. $26,605D. $28,357E. $32,188

EAR = (1 + .055/4)^4 - 1 = 5.61%; semiannual rate = 0.0561 = (1 + q/2)^2 - 1; q = 2.77% FV = 2,500*((1 + .0277)^10 - 1)/.0277 = $28,357

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

A. $19,716.67B. $20,743.77C. $24,411.81D. $24,674.60E. $25,366.63

1 = (1 + .1/2)^2 -1; q = 10.25%; 150,000 = C*[(1 - 1/{(1 + .1025)^10)}/(.1025)]; C = $24,674

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. $31,976B. $34,503C. $43,888D. $47,983E. $51,889

FV = 1,000*(1.05^22 - 1)/.05 = $38,505 - 1,000*(1.05)^17 - 1,000*(1.05)^11 = $34,503

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. $725.01B. $751.27C. $757.76D. $825.45E. $901.52

100,000 = C*[(1 - 1/{(1 + .0825/12)^360)}/(.0825/12)]; C = $751.27

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. $135,101B. $145,583C. $170,457D. $190,457E. $270,457

From previous question C = $751.27; Interest = 751.27*360 - 100,000 = $170,457

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. $24.56B. $54.88C. $100.80D. $103.28E. $106.86

100,000 = C*[(1 - 1/{(1 + .0825/12)^360)}/(.0825/12)]; C = $751.27 100,000 = C*[(1 - 1/{(1 + .0825/12)^240)}/(.0825/12)]; C = $852.07 Extra = 852.07 - 751.27 = $100.80

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; $111.57B. lower; $54.72C. higher; $9.26D. higher; $190.01E. higher; $194.59

100,000 = C*[(1 - 1/{(1 + .0825/12)^360)}/(.0825/12)]; C = $751.27 100,000 = C*[(1 - 1/{(1 + .0775/12)^180)}/(.0775/12)]; C = $941.28 Difference = 941.28 - 751.27 = $190.01 higher

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. $1,316.36B. $1,325.99C. $1,512.56D. $1,645.45E. $1,760.45

150,000 = C*[(1 - 1/{(1 + .1/12)^360)}/(.1/12)]; C = $1,316.36

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. $187,500B. $271,996C. $354,234D. $473,760E. $511,390

150,000 = C*[(1 - 1/{(1 + .1/12)^360)}/(.1/12)]; C = $1,316.36 Total = 1,316.36*360 + 37,500 = $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. $99,610B. $135,467C. $136,407D. $139,144E. $170,509

PV = 1,316.36*[(1 - 1/{(1 + .1/12)^240)}/(.1/12)]; PV = $136,407

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. $11.25B. $201.99C. $295.55D. $311.55E. $314.47

150,000 = C*[(1 - 1/{(1 + .1/12)^360)}/(.1/12)]; C = $1,316.36150,000 = C*[(1 - 1/{(1 + .1/12)^180)}/(.1/12)]; C = $1,611.91 or $295.55 more

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%

150,000 = C*[(1 - 1/{(1 + .1/12)^360)}/(.1/12)]; C = $1,316.36145,500 = 1,316.36*[(1 - 1/{(1 + r)^360)}/(r)]; r = 0.0086381EAR = (1 + .0086381)^12 - 1 = 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. $88,144B. $90,938C. $96,574D. $98,159

E. $105,159

100,000 = C*[(1 - 1/{(1 + .1/12)^360)}/(.1/12)]; C = $877.57PV = 877.57*[(1 - 1/{(1 + .1/12)^300)}/(.1/12)] = $96,574

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. $443.96B. $505.67C. $652.90D. $708.63E. $733.76

PV = 877.57*[(1 - 1/{(1 + .1/12)^300)}/(.1/12)] = $96,57496,574 = C*[(1 - 1/{(1 + .08/12)^360)}/(.08/12)]; C = $708.63

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. $111.98B. $139.36C. $143.81D. $161.82E. $168.94

100,000 = C*[(1 - 1/{(1 + .1/12)^360)}/(.1/12)]; C = $877.57

96,574 = C*[(1 - 1/{(1 + .08/12)^360)}/(.08/12)]; C = $708.63 or $168.94 less

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. $2,897.22B. $3,058.52C. $3,147.22D. $3,187.53E. $3,250.00

96,574*.03 + 250 = $3,147.22

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 monthsB. 16 monthsC. 17 monthsD. 18 monthsE. 19 months

96,574*.03 + 250 = $3,147.22; 3,147.22/168.94 = 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 monthsB. 18 monthsC. 19 monthsD. 20 monthsE. 21 months

3,147.22 = 168.94*[(1 - 1/{(1 + .08/12)^n)}/(.08/12)]; n = 20 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. $117.11B. $126.75C. $132.20D. $140.80E. $168.94

Old: 96,574 = C*[(1 - 1/{(1 + .1/12)^300)}/(.1/12)]; C = $877.57New: 96,574 = C*[(1 - 1/{(1 + .08/12)^300)}/(.08/12)]; C = $745.37Savings = 877.57 - 745.37 = $132.20

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. $3,729.03B. $4,458.40C. $5,121.24D. $6,664.91E. $7,563.01

20,000 = C*[(1 - 1/{(1 + .09)^6)}/(.09)]; C = $4,458.40

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. $10,000B. $12,000C. $14,000D. $16,000E. $20,000

Value = 20,000 - 4,000 - 2,000 - 2,000 = $12,000

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. $4,000B. $6,000C. $8,000D. $10,000E. $12,000

Value = 20,000 - 4,000 - 2,000*5 = $6,000

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. $20,000B. $24,999C. $26,750D. $27,899E. $31,872

20,000 = C*[(1 - 1/{(1 + .09)^6)}/(.09)]; C = $4,458.40; total = 6*4,458.40 = $26,750

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 1B. After payment number 2C. After payment number 3D. After payment number 4E. After payment number 5

After pmt 3: PV = 4,458.40*[(1 - 1/{(1 + .09)^3)}/(.09)]= $11,285; MV = $12,000

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 1B. After payment number 2C. After payment number 3D. After payment number 4

E. After payment number 5

After pmt 1: PV = 4,012.56*[(1 - 1/{(1 + .09)^5)}/(.09)]= $15,607.44; MV = $16,000$18,000 = C*[(1 - 1/1.09^6)/.09]; C = $4,012.56

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

YOUR ANSWER:

The suggested answer is The EAR is what you actually earn, the APR is a quoted rate. If interest is compounded during the year, the ending balance of a savings account cannot be computed directly using the APR. Also, in the case of the savings account, the EAR will always be higher than the APR as long as the account is compounded more than once a year and the interest rate is greater than zero.

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?

YOUR ANSWER:

The suggested answer is A bank would rather advertise the APR on loans since this rate appears to be lower and the EAR on savings accounts since this appears to be higher. As a consumer, the EAR is the more important rate since it represents the rate actually paid or earned.

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.

YOUR ANSWER:

The suggested answer is The second annuity weights its payments more toward

the back of the period, rather than the front, making it less valuable unless the discount rate is zero. Some students may get tripped up by the fact that the two annuities have the same total payments. This would clearly demonstrate a lack of understanding of the time value of money.

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.

YOUR ANSWER:

The suggested answer is The factors are the interest rate, payment amount, and number of payments. An increase in the payment and number of payments will increase the present value, while an increase in the interest rate will decrease the present value.

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.

YOUR ANSWER:

The suggested answer is The factors are the interest rate, payment amount, and number of payments. An increase in any of these three will increase the future value of the annuity.

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

YOUR ANSWER:

The suggested answer is It would be more meaningful for consumers to know the EAR rather than the APR. The EAR is slightly more difficult to compute and also more difficult to explain, and may add confusion to the loan process. However, regardless of the costs, it would appear that consumers would benefit from learning what the EAR is as opposed to the APR.

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?

YOUR ANSWER:

The suggested answer is This requires the students to actually use the present value formulas, setting the present value annuity equal to the present value of a perpetuity and solving for the interest rate that makes the two equivalent. The major first step is recognizing that the indifference point occurs when the two present values are equal. The break-even rate is 10%, below that rate, the perpetuity is better, while above that rate, the 10-year annuity is preferred.

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?

YOUR ANSWER:

The suggested answer is When done correctly, the left-hand side of the equation will be the formula for the future value of a lump sum, while the right-hand side will be the future value of an annuity. This suggests that one way to find the future value of an annuity is to find its present value, then find the future value of that lump sum.

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?

YOUR ANSWER:

The suggested answer is The present value of the perpetuity is $10,000, and the present value of the first 25 payments is $9,077.04, thus you should be willing to pay only $922.96 for payments 26 on, less than the value of one payment. This suggests that the value of a perpetuity is derived primarily from the payments received early in the life of the perpetuity, and the payments to be received later have little value today.

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.

YOUR ANSWER:

The suggested answer is Given this choice, most business owners would take the fixed rate loan with the predictable payment amount. If interest rates rise, the owner is obviously much better off having the fixed rate loan. If interest rates fall, the business owner can always attempt to refinance at a lower rate or repay early. In any event, the student should demonstrate an understanding of what happens to loan payments as interest rates rise and fall.