A 2-year bond with annual coupon 5%, face 100, yield 6%. What is Macaulay duration approximately?

• A. 1.60
• B. 1.95
• C. 2.20
• D. 1.75

Answer: (B)

Macaulay duration is the weighted average time to receive the bond’s cash flows, where each cash flow is weighted by its present value relative to the bond’s price. It tells you, in years, how long it effectively takes for an investor to be repaid by the bond’s cash flows at the chosen yield.

Here, the bond pays 5 at year one and 105 at year two. Discount those cash flows at the yield of 6%:

• PV of 5 at year 1: 5 / 1.06 ≈ 4.717

• PV of 105 at year 2: 105 / (1.06)^2 = 105 / 1.1236 ≈ 93.45

Price ≈ 4.717 + 93.45 ≈ 98.17.

Now the duration numerator is:

• 1 × PV of first cash flow ≈ 1 × 4.717 = 4.717

• 2 × PV of second cash flow ≈ 2 × 93.45 = 186.90

Sum ≈ 191.62

Divide by the price to get the Macaulay duration:

191.62 / 98.17 ≈ 1.95 years.

So the Macaulay duration is about 1.95 years. The result sits between 1 and 2, reflecting the two cash flows, with the later, larger payment pulling the duration closer to 2.