Towson UniversityDepartment of FinanceFin331Dr. M. Rhee2010 SpringNAME:ID#:1. If APR = 10%, what is the EAR (effective annual rate) for quarterly compounding?a. 10.00%b. 10.38%c. 12.36%d. 13.36%e. 15.52%Answer: b APR = Nominal rate 10.00%Periods/yr 4EFF% =(1+(rNOM/N))N − 1 = 10.38%2. If the current one year CD rate is 3% and the best estimate of one year CD which will be available one yearfrom today is 5%, what is the current two year CD rate with 1% liquidity premium?a. 4.0%b. 4.5%c. 5.0%d. 5.5%e. 6.0%Answer: C(1 + 0R2 – 0.01)2 = (1.03)1 × (1.05)10R2 = {(1.03) × (1.05)}1/2 + 0.01 – 1 = 4.9952% ≈ 5.00%3. Which of the following statements is CORRECT, assuming positive interest rates and holding other things constant?a. The present value of a 5-year, $250 annuity due will be lower than the PV of a similar ordinary annuity.b. A 30-year, $150,000 amortized mortgage will have larger monthly payments than an otherwise similar 20-year mortgage.c. A bank loan's nominal interest rate will always be equal to or greater than its effective annual rate.d. If an investment pays 10% interest, compounded quarterly, its effective annual rate will be greater than10%.e. Banks A and B offer the same nominal annual rate of interest, but A pays interest quarterly and B pays semiannually. Deposits in Bank B will provide the higher future value if you leave your funds on deposit.Answer: d4. You have a chance to buy an annuity that pays $550 at the beginning of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?a. $1,412.84b. $1,487.20 c. $1,565.48d. $1,643.75e. $1,725.94Answer: cBEGIN ModeN 3I/YR 5.5%PMT $550FV $0.00PV -$1,565.48Therefore, to receive $550 at the beginning of each year for 3 years at 5.5%, the fair value you should pay is $1,565.485. Your aunt has $500,000 invested at 5.5%, and she now wants to retire. She wants to withdraw $45,000 at the beginning of each year, beginning immediately. She also wants to have $50,000 left to give you when she ceases to withdraw funds from the account. For how many years can she make the $45,000 withdrawals and still have $50,000 left in the end?a. 15.54b. 16.36c. 17.22d. 18.08e. 18.99Answer: a or cBEGIN ModeDepending on how you consider the inflow and outflow of the cash flows, the answer can be a or c. 15.05 years is the correct answer (a is closest), but c is counted as the correct answer as well.6. How much do you need to save each year from two years from today and onward so that you can have $1,000 six years from today at 10% interest rate?a. $150b. $164c. $173d. $183e. $190Answer: bN=5, I/Y=10, FV=1,000 => PMT = -163.807. Jennifer can make a 100,000 down payment to buy a house. The house is $380,000 and she was offered 30-year mortgage and 15-year mortgage at a market rate of 12%. How much more interest would Jennifer pay if she took out a 30-year mortgage instead 15-year mortgage?a. $106,430b. $413,957c. $431,959d. $450,790e. $490,250Answer: cFor 30 years: N=30*12=360, I=1%, PV= -(380,000-100,000) => PMT=2,880.12INT = (2,880.12*360) – 280,000 = 756,843.20For 15 years: N=15*12=180, I=1%, PV= -(380,000-100,000) => PMT=3,360.47INT = (3,360.47*180) – 280,000 = 324,884.60Therefore, the difference in the interests is 756,843.20 - 324,884.60 = 431,958.608. How long will it take for you to pay off $1,500 charged on your credit card, if you plan to make the minimum payment of $50 per month and the credit card charges 24% per annum? a. 10 monthsb. 35 monthsc. 10 yearsd. 863 monthse. You may not be able to pay off the debtAnswer: eI = 2, PV = -1500, PMT = 20 ⇨ N = ? Error 5 is “No solution exists” in the Texas Instrument BA II Plus calculator9. 5-year Treasury bonds yield 5.5%. The inflation premium (IP) is 1.9%, and the maturity risk premium (MRP) on 5-year T-bonds is 0.4%. There is no liquidity premium on these bonds. What is the real risk-free rate, r*?a. 2.59%b. 2.88%c. 3.20%d. 3.52%e. 3.87%Answer: c Basic equation: r = r* + IP + MRP + DRP + LPrT-bond5.50%IP 1.90%MRP 0.40%LP and DRP 0.00%r* = rT-bond – IP – MRP 3.20%10. Suppose the interest rate on a 1-year T-bond is 5.0% and that on a 2-year T-bond is 7.0%. Assuming the pure expectations theory is correct, what is the market's forecast for 1-year rates 1 year from now?a. 7.36%b. 7.75%c. 8.16%d. 8.59%e. 9.04%Answer: e1-year rate today 5.00%2-year rate today 7.00%Maturity of longer bond 2Ending return if buy the 2-year bond = needed return on series of 1-year bonds 1.1449Rate of return, or yield, on a 1-year bond 1 year from now: X in this equation: (1.05)(1 + X) = 1.1449X = 1.1449/1.05 − 1 = 9.04%11. Which of the following statements is CORRECT?a. The yield on a 2 year corporate bond should always exceed the yield on a 2 year Treasury bond.b. The yield on a 3 year corporate bond should always exceed the yield on a 2 year corporate bond.c. The yield on a 2 year Treasury bond should always exceed the yield on a 2 year Treasury bond.d. If inflation is expected to increase, then the yield on a 2 year bond should exceed that on a 3 year bond.e. The real risk-free rate should increase if people expect inflation to increase.Answer: a12. Crockett Corporation's 5-year bonds yield 6.35%, and 5-year T-bonds yield 4.75%. The real risk-free rate is r* = 3.60%, the default risk premium for Crockett's bonds is DRP = 1.00% versus zero for T-bonds, the liquidity premium on Crockett's bonds is LP = 0.90% versus zero for T-bonds, and the maturity risk premium for all bonds is found with the formula MRP = (t – 1) × 0.1%, where t = number of years to maturity. What inflation premium (IP) is built into 5-year bond yields?a. 0.68%b. 0.75%c. 0.83%d. 0.91%e. 1.00%Answer: bBasic equation: r = r* + IP + MRP + DRP + LPrCrockett Not needed in this problem 6.35%LP Not needed in this problem 0.90%DRP Not needed in this problem 1.00%rT-bondRequired data 4.75%r* Required data 3.60%Years to maturity Required data 5MRP = (t – 1) × (0.1) = 0.40%IP = rT-bond − r* − MRP 0.75%13. Suppose the real risk-free rate is 3.50%, the average future inflation rate is 2.50%, a maturity premium of 0.2% per year to maturity applies, i.e., MRP = 0.20%(t), where t is the years to maturity. Suppose also that a liquidity premium of 0.50% and a default risk premium of 1.35% applies to A-rated corporate bonds. What is the difference in the yields on a 5-year A-rated corporate bond and on a 10-year Treasury bond?
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