Problem 1. Suppose that the nominal interest rate for the coming year is 9% and inflation is expected to be 5%. Compute the real interest rate for this time period. If (nominal) interest payments are taxed at a rate of 30%, what is the after-tax real interest rate?
Problem 2. Price a bond that matures in two years with face value of $1000 and coupon rate of 7% if the real interest rate is 3% and inflation is expected to be 2% for the first year of the bond’s life and 3% for the second year of the bond’s life.
Problem 3. Suppose you wish to price a consol bond, a bond with no maturity date. The bond pays $120 interest to the holder at the end of the first year, then $100 in each year of the bond’s (infinite) life after that. If the interest rate is expected to be 11% for the first year, then 10% thereafter, what is the price of this bond?
Problem 4. Suppose you work at a bank and grant a simple loan for $100 000 that requires payment of $200 000 in four years’ time. What is the yield to maturity on this loan?
Problem 5. You own a discount bond with a face value of $1000 and a current market price of $875. The bond matures in exactly one year. Calculate its yield to maturity and yield on a discount basis. Is the yield on a discount basis higher or lower than the yield to maturity? What are the sources of this understatement or overstatement?