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1

3. If you believe that the real rate of interest is 3 per cent and the expected inflation  rate is 2 per cent, what should the nominal interest rate be?

Chapter 4

i = r + ∆Pe = 3% + 2% = 5%.   The correct compounding calculation is (1.03)(1.02) - 1 = 5.06%.  
 

2

13. The one-year real rate of interest is currently estimated to be 5 per cent. The  current annual rate of inflation is 2 per cent, and market forecasts predict the  annual rate of inflation to be 4 per cent. What is the current one-year nominal  rate of interest?
 Chapter 4

Assuming the Fisher effect, the current one-year nominal rate should be 9 percent, the sum of the real rate (5%) plus the expected inflation rate (4%), an approximate but illustrative way of estimating the answer.  The correct way to deal with compounding rates is to multiply (1+.05)(1+.04) - 1 = 9.20%.

3

14. The following annual inflation rates have been forecast for the next 5 years:  year 1: 2%  year 2: 3%  year 3: 4%  year 4: 4%  year 5: 3%

Use the average annual inflation rate and a 3 per cent real rate to calculate the appropriate contract rate for a one-year and a five-year loan. How would your contract rates change if the year-1 inflation forecast increased to 4 per cent? Discuss the difference in the impact on the contract rates from the change in inflation

Chapter 4


 A lender would require compensation for both opportunity cost and loss of purchasing power.  Starting with the one-year rate, the sum of the real rate, 3%, plus the expected rate of inflation, 2%, would be roughly 5% and accurately, (1.03)(1.02) -1 = 5.06%.  The five-year rate would be the sum of the real rate plus the geometric average inflation rate expected:   (1.03)(1.03197) - 1 = 6.29%.   If the one-year expected inflation rate were 4%, the geometric average expected rate of inflation would be 3.6% and the contract rate would likely be (1.03)(1.036) -1 = 6.71%.  Nominal rates include the real rate plus the expected inflation rate.

4

16. An investor purchased a one-year Treasury security with a promised yield of 6  per cent. The investor expected the annual rate of inflation to be 2 per cent;  however, the actual rate turned out to be 6 per cent. What were the expected and  the realised real rates of return for the investor?

Chapter 4

 


 The expected real rate is re = i - Pe = 6% - 2% = 4%; the realized real rate is  rr = i - Pa = 6% - 6% = 0.

5

2. If you were to invest $100 in a savings account offering 6 per cent interest compounded quarterly, how much money would be in the account after three years?

Chapter 5

If you were to invest $100 in a savings account offering 6 per cent interest compounded quarterly, how much money would be in the account after three years?

6

3. Your rich uncle promises to give you $10 000 when you graduate from university. What is the value of this gift if you plan to graduate in five years and the interest rate is 8 per cent?

Chapter 5

3. Your rich uncle promises to give you $10 000 when you graduate from university. What is the value of this gift if you plan to graduate in five years and the interest rate is 8 per cent?

7

4. An investor purchases a $1000 par value bond with 5 years to maturity at $985. The bond pays $80 of interest annually. The investor plans to hold the bond for 2 years and expects to sell it at the end of the holding period for 94 per cent of its face value. What is this investor’s expected yield? Use the trial-and-error method.

Chapter 5
 

4. An investor purchases a $1000 par value bond with 5 years to maturity at $985. The bond pays $80 of interest annually. The investor plans to hold the bond for 2 years and expects to sell it at the end of the holding period for 94 per cent of its face value. What is this investor’s expected yield? Use the trial-and-error method.

Chapter 5

8

 7. Brennan Alston deposits $2000 in a savings account offering 6.25 per cent compounded daily. After 4 years, assuming he makes no further deposits, what will be the balance in his account?

Chapter 5

 7. Brennan Alston deposits $2000 in a savings account offering 6.25 per cent compounded daily. After 4 years, assuming he makes no further deposits, what will be the balance in his account?

Chapter 5

9

8. Find the price of a corporate bond maturing in 5 years that has 5 per cent coupons (annual payments), a $1000 face value, and an ‘AA’ rating. A local newspaper’s financial section reports that the yields on 5-year bonds are: ‘AAA’, 6 per cent; ‘AA’, 7 per cent; and ‘A’, 8 per cent.

8. Find the price of a corporate bond maturing in 5 years that has 5 per cent coupons (annual payments), a $1000 face value, and an ‘AA’ rating. A local newspaper’s financial section reports that the yields on 5-year bonds are: ‘AAA’, 6 per cent; ‘AA’, 7 per cent; and ‘A’, 8 per cent.

10

9. Find the purchase price of the following bonds assuming the market interest rate is 5.5 per cent.

Chapter 5
 

9. Find the purchase price of the following bonds assuming the market interest rate is 5.5 per cent.

Chapter 5

11

10. An investor purchases a $1000 10-year bond that pays half-yearly coupon interest of 6 per cent.  The market rate of interest at that time is 4.5 per cent.  After 5 years, the bond is sold (at this time the market rate of interest is 5.5 per cent).  Calculate the yield that the investor has earned on the investment.  

Chapter 5
 

10. An investor purchases a $1000 10-year bond that pays half-yearly coupon interest of 6 per cent.  The market rate of interest at that time is 4.5 per cent.  After 5 years, the bond is sold (at this time the market rate of interest is 5.5 per cent).  Calculate the yield that the investor has earned on the investment.  

Chapter 5

12

13. Carol Chastain purchases a 1-year discount bond with a $1000 face value for $937.97. What is the yield of the bond?

Chapter 5
 

13. Carol Chastain purchases a 1-year discount bond with a $1000 face value for $937.97. What is the yield of the bond?

Chapter 5