Question

a. Find the duration of a 6% coupon bond making annual coupon payments if it has three years until maturity and has a yield to maturity of 6%. Note: The face value of the bond is $1,000. (Do not round intermediate calculations. Round your answers to 3 decimal places.) b. What is the duration if the yield to maturity is 10%? Note: The face value of the bond is $1,000. (Do not round intermediate calculations. Round your answers to 3 decimal places.)

b. What is the duration if the yield to maturity is 10%? Note: The face value of the bond is $1,000. (Do not round intermediate calculations. Round your answers to 3 decimal places.)

Answer 1

a. Par Value =1000
Annual Coupon =6%*1000 =60
YTM =6%
Since Coupon Rate and YTM are same price is same as par value =1000
Maaculay duration =(1*Coupon/(1+YTM)+2*Coupon/(1+YTM)^2+3*(Par Value+Coupon)/(1+YTM)^3)/Price
=(1*60/1.06+2*60/1.06^2+3*1060/1.06^3)/1000 =2.83339

Modified Duration=Macaulay Duration/(1+YTM)=2.83339/(1+6%)=2.673

b. Par Value =1000
Annual Coupon =6%*1000 =60
YTM =10%
Price of Bond =PV of Coupons+PV of Par value =60*((1-(1+10%)^-3)/10%)+1000/(1+10%)^3 =900.5259
Maaculay duration =(1*Coupon/(1+YTM)+2*Coupon/(1+YTM)^2+3*(Par Value+Coupon)/(1+YTM)^3)/Price
=(1*60/1.10+2*60/1.10^2+3*1060/1.10^3)/900.5259 =2.8238

Modified Duration=Macaulay Duration/(1+YTM)=2.8238/(1+10%)=2.567