Consider a bond with a face value of $1,000, a coupon rate of 8%, and a yield to maturity of 6%. The bond pays interest semi-annually and matures in 10 years. Given the bond's characteristics, an analyst calculates its modified duration to be 7.5 years. The analyst is now estimating the price change of the bond if the yield to maturity decreases by 50 basis points (0.50%).
Using the modified duration and knowing that the bond's convexity is 105, how will the price of the bond change in response to the change in yield?