The modified duration of a bond can be estimated using the following formula:Modified Duration=##
/###Modified Duration=#y#P/Pwhere###Pis the change in the bond's price,#Pis the initial price, and###yis the change in yield.
Given:
* Initial price (P) = $87,000
* New price after yield change (P') = $84,500
* Change in price (#P) = $87,000 - $84,500 = $2,500
* Change in yield (#y) = 5.7% - 4.7% = 1% = 0.01
Modified Duration =2,500/87,0000.01=0.0287350.01=2.8735#2.880.012,500/87,000=0.010.028735=2.
8735#2.88