Effective duration is calculated using the formula:

$Effective \ Duration = \frac{P_{-\Delta y} - P_{+\Delta y}}{2 \times P_{0} \times \Delta y}$

Where:

• $P_0$ is the current price.
• $P_{-\Delta y}$ is the price when yield decreases by $\Delta y$ (Price up).
• $P_{+\Delta y}$ is the price when yield increases by $\Delta y$ (Price down).

Current price ($P_0$):

• N = 15
• FV = 100
• I/Y = 8.2
• PMT = 7
• CPT PV = 89.8529

Price when yield decreases ($P_{-\Delta y}$):

• N = 15
• FV = 100
• I/Y = 7.9 (8.2% - 30 basis points)
• PMT = 7
• CPT PV = 92.2492

Price when yield increases ($P_{+\Delta y}$):

• N = 15
• FV = 100
• I/Y = 8.5 (8.2% + 30 basis points)
• PMT = 7
• CPT PV = 87.5436

$Effective \ Duration = \frac{92.2492 - 87.5436}{2 \times 89.8529 \times 0.003} = \frac{4.7056}{0.5391174} \approx 8.73$