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.