Question

# Find the duration of a 6% coupon bond making annual coupon payments if it has three...

Find the duration of a 6% coupon bond making annual coupon payments if it has three years until maturity and a yield to maturity of 7.7%. What is the duration if the yield to maturity is 11.7%? (Do not round intermediate calculations. Round your answers to 4 decimal places.)

YTM Duration 7.7% YTM 11.7% YTM

Calculation of Duration

 PV Rate @ 7.7% Following data are available Face Value 1000 (Assume) Coupon Rate 6% Years to maturity 3 years Redemption Value 1000 Yield to maturity 7.70%

 First step : Calculate market price of bonds 60, present value 7.7% for 3 years) 60*2.59 155.4 1000, present value 7.7% for 3 years) 1000*.800 800 Market Price 955.4 Second Step: Calculation of bond Year PV @7.7% Proportion of bond Value Proportion of bond value x time 1 0.928 55.68 0.05828 0.05828 2 0.862 51.72 0.05413 0.10827 3 0.8 848 0.88759 2.66276 955.4 1 2.82931 Duration of bonds is 2.8293 years

 PV Rate @ 11.7% Face Value 1000 (Assume) Coupon Rate 6% Years to maturity 3 years Redemption Value 1000 Yield to maturity 11.70% First step : Calculate market price of bonds 60, present value 11.7% for 3 years) 60*2.4113 144.678 1000, present value 11.7% for 3 years) 1000*.7162 716.2 Market Price 860.878 Second Step: Calculation of bond Year PV @11.7% Proportion of bond Value Proportion of bond value x time 1 0.8947 53.682 0.06236 0.06236 2 0.8005 48.03 0.05579 0.11158 3 0.7162 759.172 0.88185 2.64556 860.884 1.00000 2.81949 Duration of bonds is 2.8195 years