Final answer:
The duration of a five-year zero-coupon bond is 5 years, and the duration of a twenty-year zero-coupon bond is 20 years.
Step-by-step explanation:
The duration of a zero-coupon bond is equal to the time to maturity since there are no intermediate cash flows to consider. Therefore, the duration for a five-year zero-coupon bond, which is currently trading at a 4% yield, would be 5 years. Likewise, the duration for a twenty-year zero-coupon bond, with a 3.5% yield, would be 20 years. These durations reflect the sensitivity of the bond's price to interest rate changes and are a key concept in bond valuation and yield analysis.
The duration of a zero-coupon bond is indeed equivalent to its time to maturity since zero-coupon bonds do not generate intermediate cash flows. Thus, for a five-year zero-coupon bond currently trading at a 4% yield, the duration would be 5 years. Similarly, for a twenty-year zero-coupon bond with a 3.5% yield, the duration would be 20 years. Duration serves as a critical metric in bond valuation and yield analysis, providing insight into the sensitivity of the bond's price to changes in interest rates. These examples illustrate that, for zero-coupon bonds, the duration aligns directly with the time to maturity, highlighting their unique characteristic of a single cash flow at maturity