1. Assume that monthly payments begin in one month. What will each payment be? A) $ B) $1, C) $1, D) $1, E) $1,722.

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1 Name: Date: You and your spouse have found your dream home. The selling price is $220,000; you will put $50,000 down and obtain a 30-year fixed-rate mortgage at 7.5% APR for the balance. 1. Assume that monthly payments begin in one month. What will each payment be? A) $ B) $1, C) $1, D) $1, E) $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 6.75% APR. 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; $ B) lower; $ C) higher; $ D) higher; $ E) higher; $ The interest rate expressed as if it were compounded once per year is called the: A) Stated interest rate. B) Compound interest rate. C) Effective annual rate. D) Periodic interest rate. E) Daily interest rate. 4. A loan where the borrower pays interest each period and repays the entire principal of the loan at some point in the future is called a(n) loan. A) amortized B) continuous C) balloon D) pure discount E) interest-only Page 1

2 5. Which of the following statements is FALSE? A) When comparing investments it is best not to rely solely on quoted rates. B) Compounding typically leads to differences between quoted and effective rates. C) The APR on a loan with monthly payments is less than the annual interest you actually pay. D) The APR is the interest rate per period multiplied by the number of periods per year. E) With monthly compounding, the APR will be larger than the effective annual rate. 6. You have $800 that you would like to invest. You have 2 choices: Savings account A which earns 8% compounded annually, or savings account B which earns 7.70% 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. 7. You are going to invest $500 at the end of each year for ten years. Given an interest rate, you can find the present value of this investment by: I. Adding the cash flows together and finding the present value of the sum using the appropriate present value factor. II. Applying the proper present value factor to each cash flow, then adding up these present values. III. Finding the future value of each cash flow, adding all of the future values together, then finding the discounted present value of this future value sum. IV. Finding the future 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 8. Given the following cash flows, what is the present value if the discount rate is 8%? Year Cash Flow $400 $250 $900 $1925 A) $1, B) $2, C) $2, D) $3, E) $3, Page 2

3 9. Given the following cash flows, what is the implicit discount rate if the present value is $2,450? Year Cash Flow $700 $950 $1400 A) 5.45% B) 8.72% C) 10.48% D) 12.89% E) 15.91% 10. You just won the lottery. You and your heirs will receive $40,000 per year forever, beginning one year from now. What is the present value of your winnings at an 10% discount rate? A) $ 44,000 B) $300,000 C) $387,500 D) $400,000 E) $437, What is the effective annual rate of 11% compounded semiannually? A) 11.00% B) 11.15% C) 11.30% D) 11.84% E) 12.16% 12. What is the present value of $1,500 payments received at the beginning of each year for the next 10 years? Assume an interest rate of 6.525%. A) $ B) $ 7, C) $10, D) $11, E) $15, Page 3

4 13. You are going to withdraw $5,000 at the end of each year for the next four years from an account that pays interest at a rate of 9% 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 third withdrawal is made? A) $ 4, B) $ 4, C) $ 5, D) $ 6, E) $10, You are considering investing $400 in a 12-year annuity. The rate of return you require is 9%. What annual cash flow from the annuity will provide the required return? A) $ B) $ C) $ D) $ E) $ Your brother-in-law borrowed $3,000 from you 5 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 12%, and assuming that he wishes to make 5 equal annual payments beginning in one year, how much would your brother-in-law have to pay you annually in order to pay off the debt? (Assume that the loan continues to accrue interest at 12% per year.) A) $ B) $1, C) $1, D) $1, E) $3, Moe purchases a $50 annual perpetuity for which payments begin in one year. Larry purchases a $50 annual perpetuity for which payments begin immediately. If a 12.5% interest rate is appropriate for both cash flow streams, which of the following statements is true? A) Moe's perpetuity is worth $50 more than Larry's. B) Larry's perpetuity is worth $50 more than Moe's. C) The perpetuities are of equal value today. D) Larry's perpetuity is worth $44.44 more than Moe's. E) Moe's perpetuity is worth $44.44 more than Larry's. Page 4

5 17. Vito Corleone will loan you money on a "four-for-five" arrangement; i.e., for every $4 he gives you today, you give him $5 one week from now. What is the APR of this loan? A) 250% B) 869% C) 1,000% D) 1,300% E) 1,800% 18. Four years from now you will receive the first of seven annual $6,000 payments. The current interest rate is 8%, but by the beginning of year 4, the rate will rise to 10%. What is the present value of this cash flow stream? A) $18, B) $21, C) $23, D) $26, E) $32, The preferred stock of Placer Corp. currently sells for $44.44 per share. The annual dividend of $4 is fixed. Assuming a constant dividend forever, what is the rate of return on this stock? A) 7.0% B) 8.0% C) 9.0% D) 10.0% E) 11.0% 20. You work for a furniture store. You normally sell a living room set for $4,000 and finance the full purchase price for 24 monthly payments at 24% APR. You are planning to run a zero-interest financing sale during which you will finance the set over 24 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) $4,000 B) $4,589 C) $5,076 D) $5,351 E) $6,240 Page 5

6 21. If you deposit $1,000 at the end of each six months into an account which earns 8.5% interest compounded quarterly, how much will be in the account in 6 years? A) $12, B) $13, C) $14, D) $15, E) $17, Rob and Laura wish to buy a new home. The price is $387,500 and they plan to put 20% down. New Rochelle Savings and Loan will lend them the remainder at a 9% fixed APR for 30 years, with monthly payments to begin in one month. (Ignore taxes.) 22. How much will their monthly payments be? A) $2, B) $2, C) $3, D) $3, E) $3, 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) 8.11% B) 9.00% C) 9.25% D) 9.47% E) 9.75% 24. 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, which would you prefer to see and why? 25. 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. Page 6

7 26. Should lending laws be changed to require lenders to report the EAR rather than the APR? Explain. 27. A friend who owns a perpetuity 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 a price of $1,000. At an interest rate of 10%, should you pay the $1,000 today to receive payment numbers 26 and onwards? What does this suggest to you about the value of perpetual payments? With auto loans extending 5,6,7 or more years these days, it is common for buyers who wish to trade in their cars after a few years to find themselves to be "upside down" on the loan. In other words, the outstanding principal on the car loan exceeds the value of the car being traded. Suppose you buy a new Toyota for $25,000, paying nothing down. You agree to a repayment schedule of six equal annual payments beginning one year from today. The banker's required return is 10%, compounded annually. Assume the car will lose 25% of its value the first year and further lose $3,000 each year thereafter. 28. How much will your annual payments be? A) $4, B) $5, C) $6, D) $6, E) $7, Given the depreciation schedule above, how much will the car be worth after you have made your final payment? A) $ 1,250 B) $ 3,750 C) $ 6,750 D) $ 8,250 E) $12, You have $4,000 in a savings account which earns 8% compounded monthly and $4,500 in an account which earns 6% compounded monthly. How many years will it be until the two accounts have the same balance if you do not withdraw any money? A) 3 years B) 4 years C) 5 years D) 6 years E) 7 years Page 7

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Time Value of Money. Part III. Outline of the Lecture. September Growing Annuities. The Effect of Compounding. Loan Type and Loan Amortization

Time Value of Money. Part III. Outline of the Lecture. September Growing Annuities. The Effect of Compounding. Loan Type and Loan Amortization Time Value of Money Part III September 2003 Outline of the Lecture Growing Annuities The Effect of Compounding Loan Type and Loan Amortization 2 Growing Annuities The present value of an annuity in which