A bond has a coupon rate of 4% paid semi-annually, a face value of $1,000, and 2 years to maturity. If the yield to maturity is 3%, what is the bond's approximate Macaulay Duration?

Question: A bond has a coupon rate of 4% paid semi-annually, a face value of $1,000, and 2 years to maturity. If the yield to maturity is 3%, what is the bond's approximate Macaulay Duration?

Answer options:

• 1.94 years ✅ 1.96 years
• 2.00 years
• 1.98 years

Correct answer: 1.96 years

Explanation: Macaulay Duration measures the weighted average time until a bond's cash flows are received. For a bond trading at a premium (coupon 4% > YTM 3%), its Macaulay Duration will be slightly less than its time to maturity. The calculation involves discounting each cash flow (4 coupon payments of $20 and a principal payment of $1,000) at the YTM and weighting them by their share of the bond's price. This results in approximately 1.96 years.