You are given two discount bonds of one-year and two-year maturities, with prices of 95 and 90, respectively. A third bond of three-year maturity and an annual coupon of 8% is trading at par. What is the three-year continuously-compounded zero-coupon rate?
A) 7.7%
B) 7.8%
C) 7.9%
D) 8.0%

Question

Quizplus · Accepted Answer

The three-year bond trading at par with an 8% coupon implies a yield of 8%. Using the formula for continuously compounded rates, we solve for the zero-coupon rate: $ e^{3r} = 1.08 $, giving $ r = \ln(1.08)/3 \approx 7.9\% $.

You Are Given Two Discount Bonds of One-Year and Two-Year