Question

a. Find the duration of a 7% coupon bond making annual coupon payments if it has three years until maturity and has a yield to maturity of 7%. Note: The face value of the bond is $1,000. (Do not round intermediate calculations. Round your answers to 3 decimal places.) 7% ΥTM years b. What is the duration if the yield to maturity is 8.4%? Note: The face value of the bond is $1,000. (Do not round intermediate calculations. Round your answers to 3 decimal places.) 8.4% ΥΤM years

Answer 1

= Kd Answer. (a) Coupon Rote = 7% YTM (Yield to Maturity) = 77 Years to Maturity = 3 years face value of Bond- & 1,000 Value of Bond tody ie Bo= Interest & Interest (1+kd) (tka) ² - (Interest + Redeemed Amt. (1+ka) 3 + + BoF to (1+0.07) Bo $1,000 70 (10.07)² 1070 (1+0.07)3 Duration of Bond L (1 x Interest +/2x Interest) + 3x (Interest Redemmed) AMOUNT) Boll (itka) 1 (1+ Kd)²) 1 (1+ kd)3 140 I lixzet 1000 L (1007) 1402 + 3210213 (1+0.07 (1+0.073 | 3 2.81 years

(b) If YTM (Kd) is equal to 8.4% 70 Bo= 70 (1+0.084) 1070 (1+0.084)3 (1+0.084)2 Bo - 964./29 or 964.18 2222222222PROD Duration of Bond = 1 1x Interest + 2 x Interest + Bol (1+ko)' (1+ kg)² 3.x (interest + Redemmed Amouw) (1+xd)s - gris [ 70 & 140 (1+0.084) & (1+0.084 32107 + (1+0.084) J 1X 2.80 years