Answer: 13.5

## Explanation For a perpetual bond (also known as a consol or perpetuity), the Macaulay duration can be calculated using the formula: **Macaulay Duration = (1 + y) / y** Where: - y = yield to maturity (in decimal form) Given: - Yield = 8% = 0.08 **Calculation:** Macaulay Duration = (1 + 0.08) / 0.08 Macaulay Duration = 1.08 / 0.08 Macaulay Duration = 13.5 **Why this formula works:** For a perpetual bond that pays a constant coupon forever, the duration is not infinite because the present value of distant cash flows becomes very small. The formula (1+y)/y gives the weighted average time to receive the cash flows. **Verification:** - Option A (7.4) is incorrect - this would be too low for a perpetual bond - Option B (8.0) is incorrect - this would be the modified duration, not Macaulay duration - Option C (13.5) is correct - matches our calculation **Key Concept:** For a perpetual bond, Macaulay duration is always greater than modified duration. Modified duration would be 1/y = 1/0.08 = 12.5, while Macaulay duration is (1+y)/y = 13.5.

Author: LeetQuiz .