The modified duration of a bond can be estimated using the following formula:Modified Duration=Δ????/????Δ????Modified Duration=ΔyΔP/P​whereΔ????ΔPis the change in the bond's price,????Pis the initial price, andΔ????Δyis the change in yield.

Given:

Initial price (P) = $87,000

New price after yield change (P') = $84,500

Change in price (ΔP) = $87,000 - $84,500 = $2,500

Change in yield (Δy) = 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