Question

A bond has a yield to maturity of 8 percent. It matures in 10 years. Its coupon rate is 8 percent. What is its modified duration? The bond pays coupons twice a year. (Do not round intermediate calculations. Enter your answers rounded to 2 decimal places.)

Answer 1

If Coupon rate and YTM are same, the price of bond is equal to 1000.
Coupon =8%*1000/2 =40
Semi Annual YTM =8%/2 =4%
Macaulay Duration =((40*1/(1+4%)+40*2/(1+4%)^2+40*3/(1+4%)^3+40*4/(1+4%)^4+40*5/(1+4%)^5+40*6/(1+4%)^6+40*7/(1+4%)^7+40*8/(1+4%)^8
+40*9/(1+4%)^9+40*10/(1+4%)^10+40*11/(1+4%)^11+40*12/(1+4%)^12+40*13/(1+4%)^13+40*14/(1+4%)^14+40*15/(1+4%)^15+40*16/(1+4%)^16+40*17/(1+4%)^17+40*18/(1+4%)^18+40*19/(1+4%)^19+1040*20/(1+3%)^20))/1000=14.1339

Modified Duration =(14.1339/2)/(1+4%)^2 =6.53 years