Suppose a$$ ten$-$year, $ $1$ comma $000$ bond with an $8\mathrm{.}9\%$ coupon rate and semiannual coupons is trading for $ $1$ comma $035\mathrm{.}82.$

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

b$.$ If the$$ bond's yield to maturity changes to $9\mathrm{.}7\%$APR$,$ what will be the$$ bond's price?