FINANCE

1. Some time ago you borrowed $100,000 for 10 years. The loan requires equal monthly payments of

$1,200, in arrears, plus a $20,000 balloon payment at the end of the loan. As of today, 94 payments remain to be paid. What is your current loan balance?

Answer: $88,506.58

2. Your client has $500,000 in a retirement account, and plans to make ten more annual deposits of $25,000 beginning six months from today. The account will earn 6.0% APR compounded daily. How much will be in the retirement account once the last deposit is made?

Answer: $1,216,460

3. Five years ago you bought a 5% coupon bond with a 15-year remaining maturity. At that time the bond had a yield to maturity of 6%. Today you sold the bond for $1,250. Given that the bond paid coupons semiannually, what was your effective annual rate of return on this investment? (Assume the first coupon was paid 6 months after you purchased the bond)

Answer: 11.7995%

4. Convert 9.9% APR compounded daily into an effectively equivalent APR compounded quarterly. (Show your result as a percentage to 4 decimal places.)

Answer: 10.0222%

5. Your client can buy an annuity that pays her $5,000 monthly for 10 years. The first payment will be received when she retires five years from now. If your client requires a return of 7.0% EAR, what’s the most she should pay for this annuity today?

Answer: $311,737.80

6. Your client just invested in a municipal bond with a 5.85% yield to maturity. If your client is in the 28% marginal tax bracket, what is this bond’s Equivalent Taxable Yield?

Answer: 8.125% 7. The investment firm of Cheatham & Swindler claims that if you invest $200,000 today you can receive

$1,200 every month forever. What is the EAR on this investment if the monthly payments are in arrears? Answer: 7.4424%

8. Your client has $450,000 in a retirement account, and plans to make ten more annual deposits of $25,000

beginning two years from today. The account will earn 7.0% APR compounded daily. How much will be in the retirement account once the last deposit is made?

Answer: $1,321,432

9. Three and a half years ago you bought a 5% coupon bond with a 15-year remaining maturity. At that time the bond had a yield to maturity of 4%. Today you sold the bond for $1,250. Given that the bond paid coupons semiannually, what was your effective annual rate of return (EAR) on this investment? (assume the first coupon was paid 6 months after you purchased the bond)

Answer: 7.8024%

10. If an investment earns 2.1% every 73 days, what is the EAR? Answer: 10.95% EAR

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11. Your client can buy an annuity that pays her $3,000 monthly for 5 years. The first payment will be received two years from today. If your client requires a return of 7% EAR, what’s the most she should pay for this annuity? Answer: $133,763.67

12. Some time ago you borrowed $100,000 for 10 years. The loan requires monthly payments of $1,265, in arrears, plus a $14,000 balloon payment at the end of the loan. As of today you still owe $87,981. How many monthly payments remain to be paid?

Answer: 94

13. On October 24, 2014, Amazon stock traded for $285 per share. Only 123 days later, on February 24, 2015, Amazon traded for $376 per share. If you had purchased 100 shares of Amazon on October 24, then sold it on February 24, what would have been your EAR? Amazon pays no dividends.

Answer: 127.57% EAR

14. Your client has $500,000 in a retirement account, and plans to make ten more annual deposits of $25,000 beginning 18 months from today. The account will earn 9% APR compounded monthly. What will be the account balance once the last deposit is made?

Answer: $1,668,672

15. Four years ago you bought a 5% coupon bond with a 12-year remaining maturity. At that time, the bond had a yield to maturity of 6%. Today you sold the bond for $1,148. Given that the bond paid coupons semiannually, what was your effective annual rate of return (EAR) on this investment?

Answer: 11.00% EAR

16. Suppose you borrow $200 from your roommate so you can go clubbing on South Beach. You must repay $215 two weeks from now. What EAR are you paying on this loan? Use a 365-day year.

Answer: 558.97% EAR

17. Your client can purchase an annuity that pays her $2,500 monthly for 5 years. The first payment will be received 6 years from today. If your client requires a return of 8% EAR, what’s the most she should pay for this annuity? Answer: $78,714.99

18. Some time ago you borrowed $100,000 for 10 years. The loan requires monthly payments of $1,326 plus a $10,000 balloon payment at the end of the loan. As of today, you still owe $89,896. How many payments have you made?

Answer: 22 19. Your client can purchase an annuity that pays her $2,000 monthly for 5 years. The first payment will be

received one year from today. If your client requires a return of 9% EAR, what is the present value of this investment? Answer: $89,764

20. Your client has $250,000 in a retirement account, and plans to make ten more annual deposits of $10,000 beginning nine months from today. The account will earn 7.5% EAR. What will be the account balance once the last deposit is made?

Answer: $647,497

21. What is the PV of an annuity of four $5,000 annual payments if the first payment is 219 days from today, and the required return is 8% EAR?

Answer: $17,078

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22. Three years ago you bought an 8% coupon bond with a 9-year remaining maturity. At that time, the bond had a yield to maturity of 9%. Today you sold the bond for $1,069. Given that the bond paid coupons semiannually, what was your effective annual rate of return on this investment?

Answer: 12.8457%

23. Your client has been saving $1,000 monthly, and presently has $43,000 in her account. If she can earn 8% EAR, how many additional monthly deposits of $1,000 must she make before she could start withdrawing $1,000 every month forever, assuming she will live that long. All payments are in arrears.

Answer: 70

24. The investment advisory firm of Robb & Cheatham claims that if you invest only $170,000 today you can receive $1,200 every month forever. What is the EAR on this investment if the payments are in arrears.

Answer: 8.8073%

25. If an investment earns 14.6% APR compounded daily, what is its quarterly periodic rate? (give % to 4 decimals) Answer: 3.7167%

26. Three years ago you bought a 5% coupon bond with a 7-year remaining maturity for $890. If you sold the

bond today, what would be your EAR on this investment? Assume coupons are paid semiannually and market interest rates have not changed since you bought the bond.

Answer: 7.1387% EAR

27. Your client has $250,000 in a retirement account, and plans to make ten more annual deposits of $10,000 beginning 18 months from today. The account will earn 7.25% EAR. How much will be in the account when the last deposit is made?

Answer: $661,135.51 28. Your client borrowed $300,000 with a 30-year 6% APR mortgage loan. If the current loan balance is

$227,063, how many monthly payments remain? Answer: 200

29. What is the PV0 of an annuity of ten $5,000 annual payments if the first payment is 18 months from today,

and the required return is 8% EAR? Answer: $32,283.89

30. Your client just borrowed $100,000 for 48 months. The loan requires equal monthly payments plus a

$25,000 balloon. It has an interest rate of 9% APR compounded monthly. What will be the loan balance at the end of the first year (after 12 payments)?

Answer: $83,691.63 31. Suppose you are offered an investment that pays $10,000 every 146 days, in arrears. You would receive

20 of these payments. If you can earn 7% EAR on your money, what is the most you’d be willing to pay for this investment? Answer: $152,367.91

32. Convert 0.03% per day into an effectively equivalent quarterly periodic rate (give % to 4 decimals). Answer: 2.7749% per quarter

33. An investment account grew from $10,000 to $28,450 in 5 years. Assuming a constant growth rate, how

much was in the account at the end of 27 months? Answer: $16,008

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34. Your client has $300,000 in a retirement account, and plans to make five more annual deposits of $25,000 beginning 18 months from today. The account earns 7% EAR. How much will be in the account when the last deposit is made?

Answer: $579,011.71

35. Your client has already made 43 payments on a $500,000 loan. The loan originally had a 10-year maturity, it requires equal monthly payments (in arrears) and a $100,000 balloon. The interest rate is 6% APR compounded monthly. What is the current loan balance?

Answer: $383,232.21 36. On March 1, 2013, Tesla Motors stock traded for $34.38 per share. Only 214 days later, on October 1,

Tesla traded for $193.00 per share. If you had purchased 100 shares of TSLA on March 1, then sold it on October 1, what would have been your EAR? Tesla pays no dividend.

Answer: 1,796.40% EAR 37. Your client has the opportunity to make an investment that will return $50,000 annually for five years.

The first of these annual payments will be received six months from now and the required return is 6% EAR. What is the present value of this investment?

Answer: $216,844.70 38. Three years ago you bought an 8% coupon bond with a 9-year remaining maturity for $936. If you sold

the bond today, what would be your EAR on this investment? Assume coupons are paid semiannually and market interest rates have not changed since you bought the bond.

Answer: 9.2599% 39. What’s the PV0 of $15,000 to be received 45 months from today if the required return is 8% EAR?

Answer: $11,239.63

40. Your client has $100,000 in her retirement account, and plans to make ten more annual deposits of $10,000 beginning two years from today. The account will earn 7.3% APR compounded daily. How much will be in the account when the last deposit is made?

Answer: $365,160.86 41. Convert 12% APR compounded semiannually to an equivalent APR compounded daily (% to four

decimals). Answer: 11.6556% APR compounded daily

42. Your client owes $199,715 on a 30-year 6% APR mortgage loan, compounded monthly. If the loan was originally for $250,000, how many monthly payments remain?

Answer: 220

43. You invested in Google stock, which pays no dividend. Exactly 146 days later you sold this stock for 5.75% more than you paid for it. What was your EAR?

Answer: 15.00% 44. What is the PV0 of an annuity of ten $5,000 annual payments if the first payment is nine months from

today, and the required return is 8% EAR? Answer: $34,202.18

45. Your client just borrowed $50,000 for five years. The loan requires equal annual payments of $10,000 in

arrears, plus a balloon payment of $25,939. What will be the remaining loan balance after the third annual payment is made?

Answer: $37,285

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46. You just bought a 6% coupon bond for $1105. It has a 7-year remaining maturity, a $1000 face value, and pays semiannual coupons. What will be the bond’s price 3 years from now if market interest rates increase by 2%? Answer: $991.27

47. A 10-year annuity pays $5,000 monthly, in arrears. If the required return is 9% APR compounded monthly

for the first four years, followed by 6% APR compounded monthly thereafter, what is the present value of this annuity? Answer: $411,694

48. Your client has $100,000 in her retirement account, and plans to make ten more annual deposits of

$10,000 beginning one year from today. The account will earn 7.0% APR compounded daily. How much will be in the account once the tenth deposit is made?

Answer: $341,169 49. Your client can purchase an annuity that pays her $1,000 monthly for 4 years. The first payment will be

received two years from today. If your client requires a return of 9% EAR, what is the present value of this investment? Answer: $34,296

50. Jack’s beanstalk is already 12 feet tall, and it is growing 100% taller every three days. How tall will the

beanstalk be three weeks from now? Answer: 1,536 feet tall

51. A 10-year annuity pays $2,500 per month, in arrears. The first payment is one month from today. If your

required return is 9% APR compounded monthly for the first 48 months, and 12% APR compounded monthly thereafter, what is the present value of this annuity?

Answer: $189,797.92 52. The U.S. Treasury is about to issue new 20-year bonds. Treasury bonds of the same maturity with an 8.5%

coupon rate are selling for $1125. What coupon rate should the new bond be given for it to initially sell for its $1,000 face value? U.S Treasury bonds have semiannual coupons.

Answer: 7.30% 53. You will receive $10,000 annually for 10 years. The first of these payments will be received 3 years from

today. What is the PV0 of these payments if the discount rate is 13% APR compounded daily? Answer: $40,409.56

54. You just bought a 6% coupon bond for $1,065. The bond has a 7-year remaining maturity, a $1000 face

value, and pays coupons semiannually. What will be the value of your bond 3 years from now if interest rates remain unchanged?

Answer: $1,039.81 55. Your client presently has $1 million in her retirement account earning 6% APR compounded daily. Three

months from now she will begin investing an additional $5,000 every quarter for ten years. How much will be in her retirement account once the last $5,000 deposit is made?

Answer: $2,094,011

56. The U.S. Treasury is about to issue new 12-year bonds. Existing Treasury bonds of the same maturity, with a 4% coupon rate, are presently selling at a 10% premium. If the Treasury wants its new bond to be issued at face value, what coupon rate should it be given? Treasury bonds have semiannual coupons.

Answer: 3.00%

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57. You have been offered the purchase of a contract entitling you to receive 36 monthly payments of $5,000 each. The first of these payments will be received two years from today. If you can earn 8.085% EAR on your money, what is the most you would pay for this contract today?

Answer: $137,874 58. Three years ago, you bought an 8% coupon bond with a 9-year remaining maturity for $936. Today you

sold the bond for $1,069. Given that the bond paid coupons semiannually, what was your effective annual rate of return on this investment?

Answer: 12.99% 59. If the Greenland Ice Sheet melts at a rate of 2% per year, how long until it is only ½ its present size?

Answer: 34.31 years 60. You purchased some stock. After holding it 73 days, you sold it for 5% more than you paid for it. There

were no dividends during this time. What was your Effective Annual Rate of return (EAR)? Answer: 27.63%

61. Your client will make twenty quarterly deposits of $5,000 into her retirement account earning 7.3% APR

compounded daily. If the first deposit is made one quarter from today, how much will be in the account when the last deposited is made?

Answer: $119,588.63 62. You just borrowed $500,000 for 15 years at 6% APR compounded monthly to buy a restaurant franchise.

The loan requires equal monthly payments of $3,927 (in arrears) plus a balloon payment at the end of the loan. What is the amount of the balloon payment?

Answer: $85,001.70 63. What is the present value (PV0) of a deferred annuity of 48 monthly payments of $893 each, if the first

payment is received three years from today and your required return is 9% APR compounded monthly? Answer: $27,627.15

64. Five years ago you purchased a $1,000 U.S. Treasury bond for $920. At the time of purchase it had a 12- year remaining maturity and a 6% coupon (paid semiannually). Market interest rates have decreased 2% since then. What is the current market value of your bond?

Answer: $1,058.69 65. Your client has $250,000 in his retirement account that earns 6% APR compounded monthly. He wants to

retire 15 years from now with $1 million in the account. How much must he save each month to achieve his goal? Answer: $1,328.93

66. Your client will receive ten annual payments of $10,000 which will be deposited into an account earning

7.3% APR compounded daily. If the first payment will be received one year from today, how much will be in the account when the last payment is deposited?

Answer: $141,956.03 67. You just borrowed $500,000 for 15 years at 6% APR compounded monthly to buy a restaurant franchise.

The loan is fully amortizing and requires equal monthly payments. What is the total interest you will pay over the life of this loan?

Answer: $259,471.15

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68. Your client has a contract entitling her to receive 24 monthly payments of $5,000 each. The first of these payments will be received two years from today. If your client can earn 6% APR compounded monthly on her investments, what is the value of her contract today?

Answer: $100,587.69 69. The U.S. Treasury is about to issue new 10-year bonds. Existing Treasury bonds of the same maturity,

with a 4% coupon rate, are presently trading for $922. If the Treasury wants its new bond to be issued at face value, what coupon rate should it be given? U.S. Treasury bonds have semiannual coupons.

Answer: 5.0% 70. You have the opportunity to make an investment today that will pay you $10,000 five years from now. If

you must earn 9% APR compounded monthly on your money, what is the most you would be willing to pay for this investment today?

Answer: $6,387.00 71. Your client has $100,000 in her retirement account that earns 6% APR compounded monthly. She wants

to retire 20 years from now with $1 million in the account. How much must she save each month to achieve her goal?

Answer: $1,447.88 72. You purchased some stock. After holding it for 58 days, you sold it for a 3% gain. No dividends were paid

during this period. What was your EAR? Answer: 20.44%

73. Your client has saved nothing for retirement, but he will deposit $10,000 into his retirement account once

every year for the next 20 years. The first deposit will be made one year from today. The account earns 8% APR compounded monthly. How much will be in the account 20 years from now?

Answer: $473,111.58 74. You are making equal annual payments on a 5-year, 9% loan of $80,000. How much total interest will be

paid over the entire 5-year life of the loan? Answer: $ 22,836.98

75. What is the present value (PV0) of a deferred annuity of 36 monthly payments of $800 each, if the first

payment is received one year from today and your required return is 9% APR compounded monthly? Answer: $23,172.39

76. You own a $1000 U.S. Treasury bond with a remaining maturity of 17 years. The bond has a 7% annual

coupon rate, a 6% YTM, and pays coupons semiannually. What is its current market value? Answer: $1,105.66

77. If today Jack invested $9,000 at 6.0% EAR, and Jill invested $8,000 at 8.0% EAR, how long would it take

until Jack and Jill have the same amount of money in their investment accounts? Answer: 6.3 years

78. What are the monthly payments on a $500,000 30-year mortgage loan that has an interest rate of

5.79% EAR? Answer: $2,883.59

79. If you invest $1,000 every month and earn 12% APR compounded monthly, how many deposits must you make before you can start withdrawing $1,000 every month forever…assuming you live that long?

Answer: 70

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80. An investment account grew at a constant rate from $10,000 to $28,450 in five years. How much was in the account at the end of 27 months?

Answer: $16,008 81. How many FSU freshmen does it take to change a light bulb?

Answer: None – that’s a sophomore course

Note: This document contains proprietary material that is the personal intellectual property of the instructor and protected by copyright laws. It is provided to students currently enrolled in FIN302 for their personal educational use only. Dissemination or use of this material for any other purpose or by any other party is strictly prohibited and will be considered a copyright infringement. Copyright F. R. Peterson © 2007 – 2018

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