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Fin 220 - Practice Problems Yomna Ahmed 1. Assume that you purchase a 6-year, 8 percent savings certificate for $1,000. If interest is compounded annually, what will be the value of the certificate when it matures? a. $630.17 b. $1,469.33 c. $1,677.10 d. $1,586.87 e.$1,766.33 2. A savings certificate similar to the one in the previous problem is available with the exception that interest is compounded semiannually. What is the difference between the future value of the savings certificate compounded semiannually and the one compounded annually? a. The semiannual certificate is worth $14.16 more than the annual certificate. b. The semiannual certificate is worth $14.16 less than the annual certificate. c. The semiannual certificate is worth $21.54 more than the annual certificate. d. The semiannual certificate is worth $21.54 less than the annual certificate. e. The semiannual certificate is worth the same as the annual certificate. 3. A friend promises to pay you $600 two years from now if you loan him $500 today. What annual interest rate is your friend offering? a. 7.55% b. 8.50% c. 9.54% d. 10.75% e. 11.25% 4. At an inflation rate of 9 percent, the purchasing power of $1 would be cut in half in just over 8 years (some calculators round to 9 years). How long, to the nearest year, would it take for the purchasing power of $1 to be cut in half if the inflation rate were only 4 percent? a. 12 years b. 15 years c. 18 years d. 20 years e. 23 years 5. You decide to begin saving toward the purchase of a new car in 5 years. If you put $1,000 at the end of each of the next 5 years in a savings account paying 6 percent compounded annually, how much will you accumulate after 5 years? a. $6,691.13 b. $5,637.09 c. $1,338.23 d. $5,975.32 e.$5,731.94 6. Refer to Problem 6. What would be the future value if the payments were made at the beginning of each year? a. $6,691.13 b. $5,637.09 c. $1,338.23 d. $5,975.32 e.$5,731.94 7. What would be the future value if $500 payment for 5 years and the account paid 6 percent compounded semiannually? a. $6,691.13 b. $5,637.09 c. $1,338.23 d. $5,975.32 e.$5,731.94 1 8. How much would you be willing to pay today for an investment that would return $800 each year at the end of each of the next 6 years? Assume a discount rate of 5 percent. a. $5,441.53 b. $4,800.00 c. $3,369.89 d. $4,060.55 e.$4,632.37 9. You have applied for a mortgage of $60,000 to finance the purchase of a new home. The bank will require you to make annual payments of $7,047.55 at the end of each of the next 20 years. Determine the interest rate in effect on this mortgage. a. 8.0% b. 9.8% c. 10.0% d. 5.1% e. 11.2% 10. If you would like to accumulate $7,500 over the next 5 years, how much must you deposit each six months, given a 6 percent interest rate and semiannual compounding? a. $1,330.47 b. $879.23 c. $654.23 d. $569.00 e.$732.67 11. What is the present value (t = 0) of the following cash flows if the discount rate is 12 percent? 0 1 2 3 4 12% | | | | | 0 2,000 2,000 2,000 3,000 a. $4,782.43 b. $6710.22 c. $4,221.79 d. $4,041.23 e.$3,997.98 12. What is the effective annual percentage rate (EAR) of 12 percent compounded monthly? a. 12.00% b. 12.55% c. 12.68% d. 12.75% e. 13.00% 13. A 20-year mortgage of $60,000,rate is 10%. This is an amortized loan. How much principal will be repaid in the second year? a. $1,152.30 b. $1,725.70 c. $5,895.25 d. $7,047.55 e.$1,047.55 14. The present value (t = 0) of the following cash flow stream is $11,958.20 when discounted at 12 percent annually. What is the value of the missing t = 2 cash flow? 0 1 2 3 4 12% | | | | | PV = 11,958.20 2,000 ? 4,000 4,000 a. $4,000.00 b. $4,500.00 c. $5,000.00 d. $5,500.00 e.$6,000.00 15. Your company is planning to borrow $1,000,000 on a 5-year, 15 percent, annual payment, fully amortized term loan. What fraction of the payment made at the end of the second year will represent repayment of principal? a. 57.18% b. 42.82% c. 50.28% d. 49.72% e. 60.27% 2 16. Your firm can borrow from its bank for one month. The loan will have to be “rolled over” at the end of the month, but you are sure the rollover will be allowed. The simple/annual interest rate is 14 percent, but interest will have to be paid at the end of each month, so the bank interest rate is 14 percent, monthly compounding. Alternatively, your firm can borrow from an insurance company at a simple/annual interest rate that would involve quarterly compounding. What APR would be equivalent to the rate charged by the bank? a. 12.44% b. 14.16% c. 13.55% d. 13.12% e. 12.88% 17. The U.S. government offers two treasury bonds, one selling at interest rate of 6.5%,and the other at the interest rate of 8.5%.Why would one bond sell for lower interest rate if the issuer is the same on both bonds. 18. Estimate the default and maturity premiums, given that Treasury bills interest rate is 2%,20 years Treasury bond =6% and 20 years AAA corporate bond is 9%. 19. Nominal Rate Inflation Rate Real rate using Real Rate using the Approx. equation true equation 13% 5% 3 Answers: 1. d. 0 1 2 3 4 5 6 | 8% | | | | | | -1,000 FV6 = ? input N = 6, I = 8, PV = -1000,and solve for FV = $1,586.87. 2. a. 0 1 2 3 4 5 6 Years 0 1 2 3 4 5 6 7 8 9 10 11 12 Periods 4% | | | | | | | | | | | | | -1,000 FV12 = ? input N = 12, I = 4, PV = -1000 and then solve for FV = $1,601.03. The difference, $1,601.03 – $1,586.87 = $14.16. 3. c. 0 1 k=? 2 | | | -500 600 input N = 2, PV = -500, FV = 600, and solve for I = 9.54%. 4. c. 0N = ? 4% | | 1.00 0.50 input I = 4, PV = -1.00, and FV = 0.50. Solve for N = 17.67 ≈ 18 years. 5. b. 0 1 2 3 4 5 || 6% | | | | 1,000 1,000 1,000 1,000 1,000 FVA5 = ? input N = 5, I = 6, PMT = 1000, and solve for FV = $5,637.09. 6. d. 0 1 2 3 4 5 | | 6% | | | | 1,000 1,000 1,000 1,000 1,000 FVA5 = ? switch to “BEG” mode, then input N = 5, I = 6, PMT = 1,000, and solve for FV = $5,975.32. 4 7. e. 0 3% 1 2 3 4 5 Years 0 1 2 3 4 5 6 7 8 9 10 Periods || | | | | | | | | | 500 500 500 500 500 500 500 500 500 500 FVA10 = ? input N = 10, I = 3, PMT = 500, and solve for FV = $5,731.94. 8. d. 0 1 2 3 4 5 6 5% | | | | | | | PVA = ? 800 800 800 800 800 800 input N = 6, I = 5, PMT = 800, and solve for PV = $4,060.55. 9. c. 0 1 2 3 20 k=? | | | | ••• | 60,000 7,047.55 7,047.55 7,047.55 7,047.55 input N = 20, PV = -60000, PMT = 7047.55, and solve for I = 10.00%. 10. c. 0 1 2 3 4 5 Years 0 3% 1 2 3 4 5 6 7 8 9 10 Periods || | | | | | | | | | PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT 7,500 input N = 10, I = 3, FV = 7500, and solve for PMT = $654.23. 11. b. Discount each cash flows to year zero, then add all the PVs ,i.e. 2000/1.12 +2000/(1.12^2)+2000/(1.12^3)+3000/(1.12^4), = $6710.22 12. c. EAR = (1 + APR/m)m – 1.0 = (1 + 0.12/12)12 – 1.0 5 = (1.01)12 – 1.0 = 1.1268 – 1.0 = 0.1268 = 12.68%. 13. a. Period Beginning Payment Interest Principal Ending Balance Balance Reduction 1 60,0000 7,047.55 6,000 1,047.55 58,952.45 2 58,952.45 7,047.55 5,895.25 1,152.30 57,800.15 14. e. Add 2000/(1.12)+ 4000/(1.12^3)+4000/(1.12^4) =7,174.9.Then deduct what you get from the total present value so 11,958.20-7,174.9=4,783.3.The missing cash flow has a present value of 4,783.3. 4783.3= missing cash flow /(1.12^2) Therefore, the missing cash flow is equal to 6,000. 15. a. N = 5, I = 15, PV = 1000000, to solve for PMT = $298,315.55. Period Beginning Payment Interest Principal Ending Balance expense Reduction Balance 1 1,000,000 298,315.55 150,000 148,315.55 851,684.45 2 851,684.45 298,315.55 127,752.67 170,562.88 681,121.57 The fraction that is principal is $170,562.88/$298,315.55 = 57.18%. 16. b. Start with a time line to picture the situation: Bank: APR = 14%; EAR = ? 0 1 2 3 4 5 6 7 8 9 10 11 12 | | | | | | | | | | | | | Insurance company: EAR = 14.93%; APR=? 0 1 2 3 4 | | | | | Note that simple rate is the another name for APR. EAR = (1 +APR /12)12 – 1 = (1 + 0.14/12)12 – 1 = 14.93%. 14.93% = (1 + APR/4)4 – 1 1.1493 = (1 + APR /4)4 1.0354 = 1 + APR /4 0.0354 = APR /4 APR = 14.16%. 6 17. The difference could be because of maturity risk premium. 18. Maturity Risk premium =6%-2%=4%. Default Risk premium= 9%-6%=3% 19. Approximate Real Rate 13% 5% 8% True Real Rate 1.13/1.05) 1 1.0762 1 0.0762 or 7.62% 7