A 20-year annual coupon bond is currently selling for its par value of $10,000 with an annual yield of 7%. If the bond is callable at par, what is the effective duration of the bond, assuming rates change by 2%? The price of the bond at a 9% interest rate equals $8,174.29.

Question

Quizplus · Accepted Answer

Effective duration = (P- - P+) / (2 * Δy * P0), where P- is the price if yield decreases, P+ is the price if yield increases, Δy is the change in yield, and P0 is the current price. Given P+ = $8,174.29, P0 = $10,000, and Δy = 2% or 0.02, we need to find P-. Since the bond is at par and callable at par, its price won't increase above $10,000 (the call feature caps the price). Thus, P- = P0 = $10,000. Plugging into the formula: Effective duration = ($10,000 - $8,174.29) / (2 * 0.02 * $10,000) = $1,825.71 / $400 = 4.56 years.

A 20-Year Annual Coupon Bond Is Currently Selling for Its