A bond with $3$ years to maturity and a coupon of $6\mathrm{.}25\%$ is currently selling at $$932\mathrm{.}24.$ Assume annual coupon payments. a$.$ What is its yield to maturity? b$.$ Compute its duration using Equation $5\mathrm{.}7$ and the YTM calculated above at the discount rate.c$.$ If interest rates are expected to decrease by $50$ basis points, what is the expected dollar change in price? Percentage change in price?