Question

8. A four-year bond with a yield of 8% (continuously compounded) pays a 6% coupon at the end of each year (one coupon per year).

a) What is the bond’s price?

b) What is the bond’s duration?

Answer 1

a. Coupon =6%*1000 =60
Rate =8%
Number of years =4
Bond Price =PV of coupons+PV of Par Value
=60/e^(r*1)+60/e^(r*2)+60/e^(r*3)+1060/e^(r*4)=60/e^(8%*1)+60/e^(8%*2)+60/e^(8%*3)+1060/e^(8%*4)=923.4313

b. Bond's Duration =(1*60/e^(r*1)+2*60/e^(r*2)+3*1060/e^(r*3)+4*60/e^(r*4))/Price of bond
=(1*60/e^(8%*1)+2*60/e^(8%*2)+3*60/e^(8%*3)+4*1060/e^(8%*4))/923.4313 =3.66