Question

7. Find the Macaulay 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%. ____________

What is the Macaulay duration if the yield to maturity is 10%? ______________

Answer 1

Coupon =6%*1000 =60
YTM =6%
Number of years =3
Price of Bond =PV of Coupon+PV of Par Value =60*((1-(1+6%)^-3)/6%+1000/(1+6%)^3 =1000
Macualay Duration =(Coupon*1/(1+YTM)+Coupon*2/(1+YTM)^2+(Coupon+Par Value)*3/(1+YTM)^3)/Price
=(60*1/1.06+60*2/1.06^2+1060*3/1.06^3)/1000 =2.83

YTM =10%
Price of Bond =PV of Coupon+PV of Par Value =60*((1-(1+10%)^-3)/10%+1000/(1+10%)^3 =900.5259
Macualay Duration =(Coupon*1/(1+YTM)+Coupon*2/(1+YTM)^2+(Coupon+Par Value)*3/(1+YTM)^3)/Price
=(60*1/1.10+60*2/1.10^2+1060*3/1.10^3)/900.5259 =2.82