Final answer:
The percentage change in the price of a bond with a Macaulay duration of 7.50 when the yield rises from 5.5% to 6.0% is approximately -3.75%. This is calculated using the bond duration and the change in yield.
Step-by-step explanation:
The student has asked about the impact of a change in yield on the price of a bond. Specifically, the bond has a Macaulay duration of 7.50 when it is priced to yield 5.5%. If the yield rises to 6.0%, we can estimate the percentage change in the price of the bond using the duration method.
To calculate the percentage change in the price of a bond given a change in yield, we can use the following formula:
Percentage change in price ≈ - Duration × Change in yield
Where the change in yield should be in decimal form. For an increase in the yield from 5.5% to 6.0%, the change in yield is 0.5%. Converting this into decimal form gives us 0.005. Using the given Macaulay duration of 7.50, the percentage change in price would be approximately:
Percentage change in price ≈ - 7.50 × 0.005 = -0.0375 or -3.75%
This means that if the yield on the bond increases from 5.5% to 6.0%, we would expect the price of the bond to decrease by approximately 3.75%.