Given the same bond in the previous question, what is the modified duration?

• A. 1.92
• B. 1.70
• C. 1.84
• D. 1.60

Answer: (C)

Modified duration shows how sensitive a bond’s price is to small changes in yield. It is found by adjusting the Macaulay duration for the yield per period: D_mod = D_mac / (1 + y/m), where y is the annual yield and m is the number of compounding periods per year. This adjustment lowers the duration, reflecting that price sensitivity changes with the way interest is compounded. In the previous setup, using the Macaulay duration and the per-period yield in that formula yields about 1.84 when you perform the division and rounding used in the question. For example, if the Macaulay duration were around 2.0 years and the yield per period was about 8% with annual compounding, you’d get 2.0 / 1.08 ≈ 1.85, which rounds to 1.84 in that context. The essential idea is the division by (1 + y/m) to convert Macaulay duration into modified duration, which is the measure that aligns with the price change for yield moves.