A bond with a 30 year maturity, par value of $1000 and is 8% p.a. coupon is selling at an yield to maturity of 8% p.a. The modified duration of the the bond at its yield is 11.26%, and its convexity is 212.4. If the bond's yield increases from 8% to 10%, how to calculate the new price of the bond using the duration rule and how to compare this answer with one calculated using the duration with convexity rule.?
I know the formula for Modified Duration is -1/(1 + y) * Macaulay Duration and formula for convexity is (Modified Duration)^2 - ▲ Modified Duration / ▲ y.
But since Macaulay's duration is not given, I am unable to proceed in solving this problem. Any solution would be highly helpful.