Chapters 5 and 6 HW Questions
C
Assume that interest rates on 20-year Treasury and corporate bonds are as follows: T-bond = 7.72% AAA = 8.72% A = 9.64% BBB = 10.18% The differences in these rates were probably caused primarily by: a. Maturity risk differences. b. Tax effects. c. Default and liquidity risk differences. d. Inflation differences. e. Real risk-free rate differences.
D
Assume that the current corporate bond yield curve is upward sloping, or normal. Under this condition, we could be sure that a. Inflation is expected to decline in the future. b. The economy is not in a recession. c. Long-term bonds are a better buy than short-term bonds. d. Maturity risk premiums could help to explain the yield curve's upward slope. e. Long-term interest rates are more volatile than short-term rates.
C
Assume that the rate on a 1-year bond is now 6%, but all investors expect 1-year rates to be 7% one year from now and then to rise to 8% two years from now. Assume also that the pure expectations theory holds, hence the maturity risk premium equals zero. Which of the following statements is CORRECT? a. The interest rate today on a 2-year bond should be approximately 7%. b. The interest rate today on a 2-year bond should be approximately 6%. c. The interest rate today on a 3-year bond should be approximately 7%. d. The interest rate today on a 3-year bond should be approximately 8%. e. The yield curve should be downward sloping, with the rate on a 1-year bond at 6%.
B
Assuming that the term structure of interest rates is determined as posited by the pure expectations theory, which of the following statements is CORRECT? a. An upward-sloping yield curve implies that future short-term rates are expected to decline. b. The maturity risk premium is assumed to be zero. c. Inflation is expected to be zero. d. In equilibrium, long-term rates must be equal to short-term rates. e. Consumer prices as measured by an index of inflation are expected to rise at a constant rate.
I and IV
Bank A pays 9.5% interest compounded annually on deposits, while Bank B pays 8.5% compounded daily. a. Based on the EAR (or EFF%), which bank should you use? I. You would choose Bank A because its EAR is higher. II. You would choose Bank B because its EAR is higher. III. You would choose Bank A because its nominal interest rate is higher. IV. You would choose Bank B because its nominal interest rate is higher. V. You are indifferent between the banks and your decision will be based upon which one offers you a gift for opening an account. b. Could your choice of banks be influenced by the fact that you might want to withdraw your funds during the year as opposed to at the end of the year? Assume that your funds must be left on deposit during an entire compounding period in order to receive any interest. I. If funds must be left on deposit until the end of the compounding period (1 year for Bank A and 1 day for Bank B), and you think there is a high probability that you will make a withdrawal during the year, then Bank A might be preferable. II. If funds must be left on deposit until the end of the compounding period (1 year for Bank A and 1 day for Bank B), and you have no intentions of making a withdrawal during the year, then Bank B might be preferable. III. If funds must be left on deposit until the end of the compounding period (1 day for Bank A and 1 year for Bank B), and you think there is a high probability that you will make a withdrawal during the year, then Bank B might be preferable. IV. If funds must be left on deposit until the end of the compounding period (1 year for Bank A and 1 day for Bank B), and you think there is a high probability that you will make a withdrawal during the year, then Bank B might be preferable. V. If funds must be left on deposit until the end of the compounding period (1 day for Bank A and 1 year for Bank B), and you think there is a high probability that you will make a withdrawal during the year, then Bank A might be preferable.
$8,488.25; $8,705.22; The annuity in part (b) is compounded more frequently; therefore, more interest is earned on interest
Find the future values of the following ordinary annuities: a. FV of $600 paid each 6 months for 5 years at a nominal rate of 15% compounded semiannually. Round your answer to the nearest cent. b. FV of $300 paid each 3 months for 5 years at a nominal rate of 15% compounded quarterly. Round your answer to the nearest cent. c. These annuities receive the same amount of cash during the 5-year period and earn interest at the same nominal rate, yet the annuity in Part b ends up larger than the one in Part a. Why does this occur?
C
If the pure expectations theory is correct (that is, the maturity risk premium is zero), which of the following is CORRECT? a. If the maturity risk premium is zero for Treasury bonds, then it must be negative for corporate bonds. b. An upward-sloping Treasury yield curve means that the market expects interest rates to decline in the future. c. The yield curve for corporate bonds may be upward sloping even if the Treasury yield curve is flat. d. A 5-year T-bond would always yield less than a 10-year T-bond. e. The yield curve for stocks must be above that for bonds, but both yield curves must have the same slope.
E
Kop Corporation's 5-year bonds yield 6.50%, and T-bonds with the same maturity yield 5.90%. The default risk premium for Kop's bonds is DRP = 0.40%, the liquidity premium on Kop's bonds is LP = 0.20% versus zero on T-bonds, the inflation premium (IP) is 1.50%, and the maturity risk premium (MRP) on 5-year bonds is 0.40%. What is the real risk-free rate, r*? a. 3.48% b. 3.00% c. 3.64% d. 4.96% e. 4.00%
A
Koy Corporation's 5-year bonds yield 8.00%, and 5-year T-bonds yield 5.15%. The real risk-free rate is r* = 3.0%, the inflation premium for 5-year bonds is IP = 1.75%, the liquidity premium for Koy's bonds is LP = 0.75% 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 is the default risk premium (DRP) on Koy's bonds? a. 2.10% b. 2.12% c. 2.48% d. 2.18% e. 2.16%
92.53 months; 18 months; $376
Simon recently received a credit card with an 20% nominal interest rate. With the card, he purchased an Apple iPhone 5 for $470. The minimum payment on the card is only $10 per month. a. If Simon makes the minimum monthly payment and makes no other charges, how many months will it be before he pays off the card? Do not round intermediate calculations. Round your answer to the nearest month. b. If Simon makes monthly payments of $30, how many months will it be before he pays off the debt? Do not round intermediate calculations. Round your answer to the nearest month. c. How much more in total payments will Simon make under the $10-a-month plan than under the $30-a-month plan. Do not round intermediate calculations. Round your answer to the nearest cent.
C
Suppose 10-year T-bonds have a yield of 5.30% and 10-year corporate bonds yield 6.65%. Also, corporate bonds have a 0.25% liquidity premium versus a zero-liquidity premium for T-bonds, and the maturity risk premium on both Treasury and corporate 10-year bonds is 1.15%. What is the default risk premium on corporate bonds? a. 1.34% b. 1.20% c. 1.10% d. 1.22% e. 0.86%
B
Suppose the U.S. Treasury issued $50 billion of short-term securities and sold them to the public. Other things held constant, what would be the most likely effect on short-term securities' prices and interest rates? a. Prices and interest rates would both rise. b. Prices would decline and interest rates would rise. c. Prices and interest rates would both decline. d. There is no reason to expect a change in either prices or interest rates. e. Prices would rise and interest rates would decline.
B
Suppose the interest rate on a 1-year T-bond is 5.00% and that on a 2-year T-bond is 6.90%. Assuming the pure expectations theory is correct, what is the market's forecast for 1-year rates 1 year from now? Round the intermediate calculations to 4 decimal places and final answer to 2 decimal places. a. 7.42 b. 8.83 c. 7.16 d. 8.04 e. 6.63
B
Suppose the rate of return on a 10-year T-bond is 6.90%, the expected average rate of inflation over the next 10 years is 2.0%, the MRP on a 10-year T-bond is 0.9%, no MRP is required on a TIPS, and no liquidity premium is required on any Treasury security. Given this information, what should the yield be on a 10-year TIPS? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average. a. 3.04% b. 4.00% c. 3.92% d. 4.60% e. 4.76%
E
Suppose the real risk-free rate is 2.50% and the future rate of inflation is expected to be constant at 7.00%. What rate of return would you expect on a 5-year Treasury security, assuming the pure expectations theory is valid? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average. a. 8.46% b. 11.59% c. 7.41% d. 7.70% e. 9.50%
E
Suppose the real risk-free rate is 3.00%, the average expected future inflation rate is 4.00%, and a maturity risk premium of 0.10% per year to maturity applies, i.e., MRP = 0.10%(t), where t is the years to maturity. What rate of return would you expect on a 1-year Treasury security, assuming the pure expectations theory is NOT valid? Include the cross-product term, i.e., if averaging is required, use the geometric average. (Round your final answer to 2 decimal places.) a. 8.88% b. 7.80% c. 8.95% d. 7.15% e. 7.22%
E
Suppose the real risk-free rate is 4.20%, the average expected future inflation rate is 2.50%, and a maturity risk premium of 0.10% per year to maturity applies, i.e., MRP = 0.10%(t), where t is the number of years to maturity, hence the pure expectations theory is NOT valid. What rate of return would you expect on a 4-year Treasury security? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average. a. 5.40% b. 7.53% c. 7.67% d. 6.96% e. 7.10%
C
The real risk-free rate is 3.55%, inflation is expected to be 3.60% this year, and the maturity risk premium is zero. Taking account of the cross-product term, i.e., not ignoring it, what is the equilibrium rate of return on a 1-year Treasury bond? (Round your final answer to 3 decimal places.) a. 8.442% b. 7.059% c. 7.278% d. 6.914% e. 8.224%
E
What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $1,600? a. $79.04 b. $85.28 c. $118.56 d. $89.44 e. $104.00
E
What is the PV of an ordinary annuity with 10 payments of $4,100 if the appropriate interest rate is 5.5%? a. $32,140.44 b. $31,213.31 c. $37,085.12 d. $32,449.48 e. $30,904.27
C
What is the PV of an ordinary annuity with 10 payments of $4,100 if the appropriate interest rate is 5.5%? a. $37,085.12 b. $31,213.31 c. $30,904.27 d. $32,140.44 e. $32,449.48
B
What's the present value of $11,500 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually? a. $10,678.81 b. $9,205.87 c. $9,113.81 d. $10,126.45 e. $9,574.10
E
What's the present value of $11,500 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually? a. $9,113.81 b. $10,126.45 c. $9,574.10 d. $10,678.81 e. $9,205.87
A
Which of the following statements is CORRECT? a. The cash flows for an annuity must all be equal, and they must occur at regular intervals, such as once a year or once a month. b. The cash flows for an annuity due must all occur at the ends of the periods. c. The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods. d. If some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the textbook defines as a variable annuity. e. If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an annuity.
B
Which of the following would be most likely to lead to a higher level of interest rates in the economy? a. Households start saving a larger percentage of their income. b. Corporations step up their expansion plans and thus increase their demand for capital. c. The economy moves from a boom to a recession. d. The Federal Reserve decides to try to stimulate the economy. e. The level of inflation begins to decline.
E
You are considering investing in a bank account that pays a nominal annual rate of 7%, compounded monthly. If you invest $3,000 at the end of each month, how many months will it take for your account to grow to $200,000? a. 61.00 b. 66.65 c. 52.53 d. 65.52 e. 56.48
C
You deposit $1,125 today in a savings account that pays 6% interest, compounded annually. How much will your account be worth at the end of 25 years? a. $3,669.55 b. $5,842.31 c. $4,828.35 d. $4,876.64 e. $5,456.04
C
You have a chance to buy an annuity that pays $1,400 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. $3,945.00 b. $3,745.76 c. $3,984.85 d. $4,781.82 e. $4,223.94
C
You have a chance to buy an annuity that pays $1,400 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. $3,945.00 b. $4,223.94 c. $3,984.85 d. $4,781.82 e. $3,745.76
$22,083.15; $25,678.02
You have saved $4,000 for a down payment on a new car. The largest monthly payment you can afford is $450. The loan will have a 9% APR based on end-of-month payments. a. What is the most expensive car you could afford if you finance it for 48 months? Round your answer to the nearest cent. b. What is the most expensive car you could afford if you finance it for 60 months? Round your answer to the nearest cent.
C
Your Aunt Ruth has $520,000 invested at 6.5%, and she plans to retire. She wants to withdraw $40,000 at the beginning of each year, starting immediately. How many years will it take to exhaust her funds, i.e., run the account down to zero? a. 25.79 b. 23.29 c. 25.04 d. 29.55 e. 24.79
B
Your aunt is about to retire, and she wants to sell some of her stock and buy an annuity that will provide her with income of $53,000 per year for 30 years, beginning a year from today. The going rate on such annuities is 7.25%. How much would it cost her to buy such an annuity today? a. $493,950.47 b. $641,494.12 c. $756,963.06 d. $647,909.06 e. $519,610.24
A
Your girlfriend just won the Florida lottery. She has the choice of $15,900,000 today or a 20-year annuity of $1,050,000, with the first payment coming one year from today. What rate of return is built into the annuity? Disregard taxes. a. 2.81% b. 3.23% c. 2.84% d. 2.16% e. 2.28%
D
Your sister turned 35 today, and she is planning to save $85,000 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund that's expected to provide a return of 7.5% per year. She plans to retire 30 years from today, when she turns 65, and she expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can she spend each year after she retires? Her first withdrawal will be made at the end of her first retirement year. a. $749,039.41 b. $756,924.04 c. $607,116.15 d. $788,462.54 e. $898,847.29
D
Your sister turned 35 today, and she is planning to save $85,000 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund that's expected to provide a return of 7.5% per year. She plans to retire 30 years from today, when she turns 65, and she expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can she spend each year after she retires? Her first withdrawal will be made at the end of her first retirement year. a. $749,039.41 b. $898,847.29 c. $607,116.15 d. $788,462.54 e. $756,924.04
Answer in files (A) - Part C = I
a. Complete an amortization schedule for a $16,000 loan to be repaid in equal installments at the end of each of the next three years. The interest rate is 12% compounded annually. Round all answers to the nearest cent. b. What percentage of the payment represents interest and what percentage represents principal for each of the three years? Round all answers to two decimal places. c. Why do these percentages change over time? I. These percentages change over time because even though the total payment is constant the amount of interest paid each year is declining as the remaining or outstanding balance declines. II. These percentages change over time because even though the total payment is constant the amount of interest paid each year is increasing as the remaining or outstanding balance declines. III. These percentages change over time because even though the total payment is constant the amount of interest paid each year is declining as the remaining or outstanding balance increases. IV. These percentages change over time because even though the total payment is constant the amount of interest paid each year is increasing as the remaining or outstanding balance increases. V. These percentages do not change over time; interest and principal are each a constant percentage of the total payment.
$5,632.97; $4,282.44
a. You plan to make five deposits of $1,000 each, one every 6 months, with the first payment being made in 6 months. You will then make no more deposits. If the bank pays 8% nominal interest, compounded semiannually, how much will be in your account after 3 years? Round your answer to the nearest cent. b. One year from today you must make a payment of $9,000. To prepare for this payment, you plan to make two equal quarterly deposits (at the end of Quarters 1 and 2) in a bank that pays 8% nominal interest compounded quarterly. How large must each of the two payments be? Round your answer to the nearest cent.