The following table shows the prices of a sample of Treasury bonds, all of which have coupon rates of zero. Each bond makes a single payment at maturity.
Years to Maturity Price (% of face value) 1 98.352% 2 94.851 3 91.044 4 86.980
a. What is the 1-year interest rate? Note: Do not round intermediate
b. What is the 2-year interest rate? Note: Do not round intermediate
c. What is the 3-year interest rate? Note: Do not round intermediate
d. What Is the 4-year Interest rate? Note: Do not round intermediate
calculations. Enter your answer as a percent rounded calculations. Enter your answer as a percent rounded calculations. Enter your answer as a percent rounded
to 2 decimal places. to 2 decimal places. to 2 decimal places.
calculations. Enter your answer as a percent rounded to 2 decimal places.
e. Is the yield curve upward-sloping, downward-sloping. or flat?
f. Is this the usual shape of the yield curve?
a. Interest rate b. Interest rate c. Interest rate • d. Interest rate e. Is the yield curve upward-sloping, downward-sloping, or flat? f. Is this the usual shape of the yield curve?
Calculation of the 1-year interest rate
a. To calculate the 1-year interest rate, we can use the formula:
Price = (Face Value) / (1 + Interest Rate)
Rearranging the formula:
Interest Rate = ((Face Value) / Price) - 1
Plugging in the values:
Interest Rate = ((100) / 98.352) - 1
Interest Rate = 1.65%
b. Using the same formula, we can calculate the 2-year interest rate:
Interest Rate = ((100) / 94.851) - 1
Interest Rate = 5.37%
c. For the 3-year interest rate:
Interest Rate = ((100) / 91.044) - 1
Interest Rate = 9.99%
d. Lastly, for the 4-year interest rate:
Interest Rate = ((100) / 86.980) - 1
Interest Rate = 15.02%
e. Based on the given data, we can observe that the yield curve is downward-sloping. This is because as the time to maturity increases, the interest rates are decreasing.
f. No, this is not the usual shape of the yield curve. Typically, a normal yield curve is upward-sloping, indicating that longer-term bonds have higher interest rates compared to shorter-term bonds. However, in this case, the yield curve is inverted or downward-sloping, where shorter-term bonds have higher interest rates than longer-term bonds.