Question $7[10$ points$]$

Suppose a $10-$year, $$1,000$ bond with a $4\%$ coupon rate and semiannual coupons is trading for a

price of $$1,123\mathrm{.}61.$

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 $6\%$ APR, what will the bond's price be$?$

c$)$ If the coupon rate were $3\%$ but everything else stayed the same, would the price change

from part a$)$ to part b$)$ be larger or smaller $($on a percentage basis$)?($Hint: no calculations

needed$)$