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

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 =

Modified Duration=Macaulay Duration/(1+YTM)=

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