Find the duration of a 6% coupon bond making annual coupon payments if it has th

Question

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.)

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.)

Explanation / Answer

Answer :

Duration of Bond when Yield to Maturity (YTM) = 7.7% ,

Coupon rate (C)= 6% ,

Years to maturity ( t) = 3

Bond Duration = (1+YTM) / YTM - ((1+YTM)+ t ( C-YTM) ) / ( C (1+YTM)^t -1) + YTM )

= (1+0.077) / 0.077 - ((1+0.077)+3(0.06-0.077)) / ( 0.06*(1+0.077)^3 - 1) + 0.077 )

= 1.077/0.077 - (1.026 / 0.0919546)

= 13.9870 - 11.15768

= 2.8293

Duration of Bond when Yield to Maturity (YTM) = 11.7 % ,

Bond Duration = (1+YTM) / YTM - ((1+YTM)+ t ( C-YTM) ) / ( C (1+YTM)^t -1) + YTM )

= 1.117 / 0.117 - (( 1.117+ 3 * ( 0.06- 0.117 )) / ( 0.06* ( 1.117^3 -1 ) + 0.117)

= 9.5470 - 0.946 / 0.14062

=9.5470 - 6.7274

= 2.8196

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