Explanation

Effective duration measures the sensitivity of a bond's price to changes in interest rates. The formula for effective duration is:

$\text{Effective Duration} = \frac{V_- - V_+}{2 \times V_0 \times \Delta y}$

Where:

• $V_-$ = Price when yield decreases (132.41)
• $V_+$ = Price when yield increases (127.66)
• $V_0$ = Current price (130.00)
• $\Delta y$ = Change in yield (0.0025 or 25 basis points)

Plugging in the values:

$\text{Effective Duration} = \frac{132.41 - 127.66}{2 \times 130.00 \times 0.0025}$ $= \frac{4.75}{2 \times 130.00 \times 0.0025}$ $= \frac{4.75}{0.65}$ $= 7.3077$

Rounding to one decimal place gives 7.3, which matches option A.

Key points:

• Effective duration is calculated using the bond's price at different yield levels
• The denominator uses the current price multiplied by twice the yield change
• This calculation assumes a parallel shift in the yield curve
• The result of 7.3 indicates the bond's price will change by approximately 7.3% for a 100 basis point change in yield