Answer: 13.5

## Explanation For a perpetual bond (also called a consol), the Macaulay duration is calculated as: **Duration = (1 + y) / y** Where: - y = yield to maturity (in decimal form) Given: - Yield = 8% = 0.08 **Calculation:** Duration = (1 + 0.08) / 0.08 Duration = 1.08 / 0.08 Duration = 13.5 **Key Points:** 1. Perpetual bonds have no maturity date and pay coupons forever 2. The Macaulay duration formula for perpetuities is derived from the weighted average time to receive cash flows 3. For a perpetual bond, duration is independent of the coupon rate and depends only on the yield 4. The higher the yield, the lower the duration (inverse relationship) **Verification:** - Option A (7.4) is incorrect - this would be too low for an 8% yield - Option B (8.0) is incorrect - this would be the modified duration, not Macaulay duration - Option C (13.5) is correct - matches our calculation **Additional Insight:** - Modified duration for a perpetual bond = 1/y = 1/0.08 = 12.5 - Macaulay duration = Modified duration × (1 + y) = 12.5 × 1.08 = 13.5

Author: LeetQuiz .