You have a bond with $24$ years to maturity, a semiannual coupon rate of $10\%$ and a market interest rate of $8\%.$ Using duration and convexity $($Macaulay$,$ modified and effective$),$ what is the expected change in the bond$$s price if the YTM rises by $100$ basis points. Compare your answer with the price you calculate for the bond$$s new price.