Suppose a $10-$year, $$1,000$ bond with an $82\%$ coupon rate and semi$-$annual coupons is trading for a price of $$1,034,62.$

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

b$.$ If the bond's yield to maturity changes to $9\mathrm{.}6\%$ APR, what will the bond's price be$?$