suppose a $10$ year, $$1000$ bond with an $8\mathrm{.}2\%$ coupon rate and semi$-$annual coupons is trading for a price of $$1034\mathrm{.}97.$

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$?$