You buy a $10-$year bond with an annual coupon'rate of $10\%$ that pays coupons twice a year with a face value of $$1000.$ The current yield$-$to$-$maturity is $9\%$ annually.

a$)$ If its yield to maturity decreases by $2\%,$ by what percentage will the price of the bond change? $(1\mathrm{.}5$ Points$)$

b$)$ If its yield to maturity increases by $2\%,$ by what percentage will the price of the bond change? $(1\mathrm{.}5$ Points$)$