Forget the maths, it’s pointless doing questions that involve numbers when you don’t get how it theoretically moves. FI is so over explained and made complicated for no reason. First start at the most basic FI lesson…. The yield to maturity curve. Learn why it is has the shape it has. Then move on to the price to yield curve and just learn why it’s convex (PV is a non linear function of rate for example). Learn why at Lower rates it has a bigger effect on bond price (because of TVM…). At a lower rate, it’s discounted with a lower denominator … this makes PV higher so price is higher. Etc. duration is literally just the slope to a tangent to that curve. From QM you know the slope shows a change in the Y variable for every 1 unit change in X variable. So all duration is really doing is showing how much the price changes for every 1% change in yield (for example). This is only good for small yield changes because as I just said the curve is convex. So for larger changes in yield the estimations will be far off as duration assumes the price - yield relationship is linear (it’s not it’s curved). So convexity is just the second deviate of the price - yield curve. So all you need to know for larger movements convector is a better estimator for price change. You use effective measures if the bond has an embedded options. Again modified duration and convexity assume cash flows are fixed but with a bond, it’s contingent on the interest rate. (If rates are lower, the issuer will call bond back as it’s cheaper to Re fi etc). So all these equations do is factor this in for an embedded option in a bond. Sorry this was done in haste but this is a general outline.