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