Assume that all bonds pay annual coupons and have par values of $$1,000.$ Assume that P$/$E ratios are computed using current price and expected earnings $($rather than current earnings$),$ and that all earnings and dividend values are annual values. An eight$-$year, $4\mathrm{.}0\%$ bond has a YTM of $4\mathrm{.}8\%,$ a duration of $6\mathrm{.}97$ and convexity of $59\mathrm{.}78.$ SHOW WORK

a$.$ Compute the percentage change in the bond$$s price if its YTM increases to $5\mathrm{.}5\%.$

b$.$ Estimate the percentage change in the bond$$s price using modified duration $($the duration rule$)$ if its YTM rises to $5\mathrm{.}5\%.$

c$.$ Estimate the percentage change in the bond$$s price using modified duration and the convexity correction $($the duration & convexity rule$)$ if its YTM rises to $5\mathrm{.}5\%.$

d$.$ Estimate the percentage change in the bond$$s price using the duration & convexity rule if its YTM falls to $4\mathrm{.}1\%.$