or all questions and problems, unless specifically otherwise noted in the question, assume that interest rates (i.e., I/Y) are greater than 0% and number of years (i.e., N) is greater than 0. Part I: Multiple Choice Questions (choose the BEST multiple-choice answer for each question). 1. TRUE or FALSE: "If the discount (or interest) rate were negative (e.g., negative 3.5%), the present value of an expected series of future cash flows would be less than the sum of the cash flows." a. True b. False 2. TRUE or FALSE: "As the interest rate decreases, the future value of future cash flows increases." a. True b. False 3. TRUE or FALSE: "If a bank compounds savings accounts quarterly, the effective rate will exceed the effective nominal rate." a. True b. False 4. TRUE or FALSE: "Suppose Jerimiah plans to invest $1,000. He can invest in Security A, which offers a 12% nominal annual return, but with daily compounding (assume 365 days per year) or he can invest in Security B which offers a 6% nominal annual return, but with semiannual compounding. After 12 years, the future value of Security A will be more than twice the future value of Security B." a. True b. False 5. TRUE or FALSE: "For a monthly amortized mortgage loan, a higher percentage of the fixed monthly payment goes to reduce the outstanding principal in the early years of the loan and percentage of the fixed monthly payment that goes to reduce principal declines in the loan's later years." a. True b. False6. TRUE or FALSE: "The present value of a future sum of money decreases as the number of years before the payment is received increases." a. True b. False 7. TRUE or FALSE: "The future value of a perpetuity of any amount (payment > 0) with any interest rate greater than 0% is infinity." a. True b. False 8. You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would decrease the calculated value of the investment? a. The cash flows are in the form of a deferred annuity, and they sum to $100,000. You learn that the annuity lasts for only 5 rather than 10 years, hence that each payment is for $20,000 rather than for $10,000. b. The interest rate increases. c. The riskiness of the investment's cash flows decreases. d. The total amount of cash flows remains the same, but more of the cash flows are received in the earlier years and less of the cash flows are received in the later years. e. The interest rate decreases. 9. Each of the following investments has a present value that can be used to determine which is most valuable (i.e., has the largest PV), which is least valuable (has the smallest PV), and which has a value in the middle of the others (has a PV that ranks 3rd if the PVs are listed from smallest to largest). Assuming a positive interest rate and assuming that all options have the same risk, which of the following is least valuable? a. Receiving $20,000 today. b. Receiving 10 payments of $2,000 per year with the first payment to be received today. c. Receiving $4,000 per year for five years beginning next year. d. Receiving $10,000 today and $10,000 next year. e. Receiving 10 payments of $2,000 per year with the first payment to be received exactly one year from today. 10. A $50,000 loan is to be amortized over 7 years, with annual end-of-year payments. Which of these statements is CORRECT? a. The annual payments would be larger if the interest rate were lower. b. If the loan were amortized over 10 years rather than 7 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 7-year amortization plan. c. The proportion of each payment that represents interest as opposed to repayment of principal would be lower if the interest rate were lower. d. The last payment would have a higher proportion of interest than the first payment. e. The proportion of interest versus principal repayment would be the same for each of the 7 payments.11. Currently, Juan has $600 in his savings account. How much would he have after 9 years if his account pays 5.6% p.a., but with monthly compounding? a. $970.28 b. $992.03 c. $927.85 d. $1001.68 e. None of the answers listed above is within $0.10 of the correct answer. 12. Exactly six years ago, Xen borrowed $480,000 to buy a house. The fixed annual interest rate on the 30- year loan is 7.25% p.a. The loan requires monthly payments, the first payment was made exactly one month after Xen bought the house, and Xen has made every payment for the past six years on time. Because interest rates have recently decreased, Xen is considering refinancing the loan. Assuming that Xen just made the 84th payment on the loan, what is the remaining balance on the loan (i.e., the amount that Xen would need to refinance to completely pay off the current loan)? a. $415,236.60 b. $479,491.64 c. $471,367.55 d. $439,181.84 e. None of the answers listed above is within $1.00 of the correct answer. 13. Your neighbor offers you an investment opportunity, which will pay a single lump sum of $1,200 eight years from today. The investment requires a single payment of $500 today. The return on the investment is ____% a. 11.565 b. 11.296 c. 11.361 d. 11.922 e. None of the answers listed above is within 0.010 percentage points of the correct answer. 14. For an annuity due of $325 per year for 10 years, which of the following interest rates will result in the smallest present value? a. 11.0%, compounded continuously. b. 11.2%, compounded daily (365 days per year). c. 11.4%, compounded monthly. d. 11.6%, compounded quarterly. e. 11.8%, compounded semiannually. f. 12.0%, compounded annually. 15. For an annuity due of $325 per year for 10 years, which of the following interest rates will result in the largest future value? a. 7.25%, compounded continuously. b. 7.30%, compounded daily (365 days per year). c. 7.35%, compounded monthly. d. 7.40%, compounded quarterly. e. 7.45%, compounded semiannually. f. 7.50%, compounded annually.16. Ryo and Tallie are shopping for furniture. They just selected a living room set that costs $7,845.00 (including tax and delivery fees). The furniture store has offered to accept payments of $205.00 per month for the next 48 months (with the first payment due exactly one month from today). What is the nominal annual rate of interest (i.e., the p.a. rate) that the furniture store is charging Ryo and Tallie (expressed as a percent and rounded to 2 decimal places)? a. 9.66% b. 11.51% c. 11.59% d. 10.84% e. 12.01% 17. Kerri James is considering the purchase of a car, which will cost her $26,400. She will borrow the entire purchase price and make monthly payments over the next six years. The first payment is due next month and the interest rate is 3.0%. She will owe $____ on the car immediately following the 18th payment. a. 17,397.75 b. 18,858.19 c. 19,508.99 d. 20,238.06 e. 21,348.72 18. Henri has $5,000 invested in a bank that pays 4.5% annually. How long will it take for Henri's funds to triple? a. 23.70 years b. 22.10 years c. 19.36 years d. 24.96 years e. None of the answers is this list is within 0.10 years of the correct answer. 19. Expo, Inc. wants to have $4,000,000 in an account exactly 10 years from today. The company will deposit $450,000 today, and they will make equal quarterly payments beginning next quarter and ending in 10 years. The account earns 8.00% p.a., compounded quarterly. The deposits must be $__________. a. 39,127.33 b. 40,528.31 c. 43,726.42 d. 49,772.90 e. 51,111.22 20. You wish to buy a truck today for $35,000. You plan to put 15% down and finance the rest at 6.00% for four years. You will make equal monthly payments of $_______. a. 698.68 b. 740.04 c. 804.52 d. 849.69 e. 905.0521. The effective annual rate of 8.25% compounded continuously is _____% . a. 9.22 b. 9.31 c. 9.38 d. 9.42 e. 9.54 22. An investment will pay $37,000 per year forever. If the relevant rate is 10% compounded monthly, the investment is worth $______ today. a. 305,597.01 b. 317,604.75 c. 329,154.33 d. 341,852.79 e. 353,346.54 23. The value today of receiving $350,000 in 22 years is $______. Assume a 5.00% interest rate. a. 119,647.45 b. 113,615.27 c. 123,737.37 d. 127,801.72 e. 131,911.32 24. You want to buy a new ski boat exactly 5 years from now, and you plan to make 5 deposits of $6,250 per year, with the first deposit made today. You will deposit your savings in an account that pays 5.2% interest. How much will you have to buy your boat exactly 5 years from today? a. $36,821.14 b. $35,197.93 c. $34,673.44 d. $36,491.41 e. None of the answers listed above is within $1.00 of the correct answer. 25. In the following table, "???" is a missing cash flow. If, at an interest rate of 9.25% p.a., the present value of the following cash flow stream is $16,500, what is the missing cash flow? Year Cash Flow 1 8,250 2 ??? 3 6,400 a. $4,640.39 b. $5,017.32 c. $4,461.88 d. $4,822.43 e. $4,245.72