Suppose a ten$-$year, $$1,000$ bond with an $8\mathrm{.}8\%$ coupon rate and semiannual coupons is trading for $$1,034\mathrm{.}78.$

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 $9\mathrm{.}6\%$ APR, what will be the bond's price?