"The $1-$year, $2-$year, and $3-$year par rates are $4\mathrm{.}63\%,4\mathrm{.}42\%$ and $4\mathrm{.}31\%$ respectively

a$.$ Price a $5\mathrm{.}2\%3-$year bond that pays annual coupons

b$.$ Use the effectuve duration and effective convexity to find the percentage change in the bonds price is the par rate is shifted upwards by $50$ bp $"$