If a bond has a Macaulay duration of 2.0 years and yields 6%, what is its approximate modified duration?

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Multiple Choice

If a bond has a Macaulay duration of 2.0 years and yields 6%, what is its approximate modified duration?

Explanation:
Modified duration shows how sensitive a bond’s price is to changes in yield, and it adjusts Macaulay duration for the yield’s compounding. The formula is D_mod ≈ D_mac / (1 + y/m). With annual yields (compounding once per year), m = 1, so D_mod ≈ 2.0 / (1 + 0.06) = 2.0 / 1.06 ≈ 1.887, which rounds to 1.89. This is why the approximate modified duration is 1.89.

Modified duration shows how sensitive a bond’s price is to changes in yield, and it adjusts Macaulay duration for the yield’s compounding. The formula is D_mod ≈ D_mac / (1 + y/m). With annual yields (compounding once per year), m = 1, so D_mod ≈ 2.0 / (1 + 0.06) = 2.0 / 1.06 ≈ 1.887, which rounds to 1.89. This is why the approximate modified duration is 1.89.

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