Question

what is the macaulay duration of a 7 percent coupon bond with five years to maturity and a current price of $1,025.30? What is the modified duration?

Answer 1

Coupon =7%*1000 =70
Par Value =1000
Price =1025.30
YTM using Excel formula =RATE(5,70,-1025.30,1000) =6.393%
Maculay Durauion =(PV of Coupon 1 * Year1 +PV of Coupon 2 * Year2+PV of Coupon 3 * Year 3+PV of Coupon 4 * Year 4+PV of Coupon 5 * Year 5 +Par Value*Year 5)/Price =(70/(1+6.393%)*1+70/(1+6.393%)^2*2+70/(1+6.393%)^3*3+70/(1+6.393%)^4*4+1070/(1+6.393%)^5*5)/1025.30 =4.3957 or 4.40 years

Modified Duration =Macaulay Duration/(1+YTM) =4.3957/(1+6.393%) =4.13 Years