A bond has a Macaulay duration equal to 6 years and a yield to maturity of 9 percent. What is the percentage change in price of a bond if yield to maturity rises to 9.5 percent?

To determine the percentage change in the bond price when the yield to maturity (YTM) rises from 9% to 9.5%, we use the duration approximation formula:

$$\text{Percentage change in price}=-\text{Macaulay Duration}\times \frac{\Delta \text{YTM}}{1+\text{YTM}}$$

Where:

• Macaulay Duration = 6 years
• Initial YTM = 9% (0.09)
• Change in YTM ($\Delta \text{YTM}$) = 9.5% - 9% = 0.5% (0.005)

Substituting the values:

$$\text{Percentage change}=-6\times \frac{0.005}{1+0.09}=-6\times \frac{0.005}{1.09}=-6\times 0.004587\approx -0.02752$$

Converting to percentage:

$$\text{Percentage change}=-2.752\%$$

Thus, the bond price decreases by approximately 2.75%.