To determine the investment horizon when the duration gap is zero, we use the relationship between modified duration and Macaulay duration:

• Modified Duration (ModDur) = Macaulay Duration (MacDur) / (1 + yield to maturity).

• Given ModDur = 7.4 and yield to maturity = 9%, we calculate MacDur as follows:

  MacDur = ModDur × (1 + yield) = 7.4 × (1 + 9%) = 8.07 years.

Since the duration gap is zero, the investment horizon equals the Macaulay duration. Therefore, the investment horizon is closest to 8.1 years.

Why not A or B?

• A (6.8 years): Incorrect because it results from dividing ModDur by (1 + yield), which misinterprets the relationship.
• B (7.4 years): Incorrect because it confuses ModDur with MacDur, leading to an incorrect horizon.