A five$-$year, $6\mathrm{.}5\%$ bond with a YTM of $5\mathrm{.}0\%$ has a duration of $4\mathrm{.}45$ and convexity of $25\mathrm{.}59.$ The bond$$s current price quote is $106\mathrm{.}494.$ Assume the bond pays annual coupons and has a par value of $$1\mathrm{.}000.$

a$.)$Compute the percentage change in the bond$$s price if its YTM increases $60$ basis points.

b$.)$ Estimate the percentage change in the bond$$s price using modified duration and the convexity correction $($the duration & convexity rule$)$ if the bond$$s YTM increases $60$ basis points.

c$.)$Compute the percentage change in the bond$$s price if its YTM decreases $75$ basis points.

d$.)$Estimate the percentage change in the bond$$s price using modified duration and the convexity correction $($the duration & convexity rule$)$ if the bond$$s YTM decreases $75$ basis points.