Suppose a $10-$year, $10\%,$ semiannual coupon bond with a par value of $$1,000$ is currently selling for $$1,135\mathrm{.}90.$ However, it can be called after $4$ years for $$1,050.$

$(1)$ What is the bond's yield to maturity $($YTM$)?(4$ points$)$

$(2)$ What is the bond's yield to call $($YTC$)?(4$ points$)$

$(3)$ If you bought this bond, do you think you would be more likely to earn the YTM or the YTC$?$ Why? $(2$ points$)$