Suppose a $10-$year, $$1,000$ bond with a coupon rate of $8\mathrm{.}1\%$ and semiannual coupons is trading for $$1,035\mathrm{.}65.$

a$.$ What is the bond's yield to maturity $($expressed as an APR with semiannual compounding$)?$

b$.$ If the bond's yield to maturity changes to $9\mathrm{.}8\%$ APR, what will be the bond's price?