First, we calculate the bond's price and Macaulay duration. Assuming an annual coupon payment, the cash flows (CF) are USD 6 for years 1 and 2, and USD 106 (coupon + principal) for year 3. The discount rate (yield) $y$ is 5%.

Step 1: Calculate Present Values (PV) of Cash Flows

• Year 1: $PV_1 = 6 / (1 + 0.05)^1 = 5.714$
• Year 2: $PV_2 = 6 / (1 + 0.05)^2 = 5.442$
• Year 3: $PV_3 = 106 / (1 + 0.05)^3 = 91.567$

Total Bond Price ($P$) = $5.714 + 5.442 + 91.567 = 102.723$

Step 2: Calculate Macaulay Duration (MacD) $MacD = \sum \frac{t \times PV_t}{P}$

• Year 1 weight: $1 \times 5.714 = 5.714$
• Year 2 weight: $2 \times 5.442 = 10.884$
• Year 3 weight: $3 \times 91.567 = 274.701$

Sum of time-weighted PVs = $5.714 + 10.884 + 274.701 = 291.299$$MacD = 291.299 / 102.723 \approx 2.8357$ years

Step 3: Calculate Modified Duration (ModD) $ModD = \frac{MacD}{1 + y} = \frac{2.8357}{1 + 0.05} = \frac{2.8357}{1.05} \approx 2.7007$

Rounding to two decimal places, the modified duration is 2.70.