A $10-$year $$1000-$par $6\%$ coupon bond has a YTM of $8\mathrm{.}5\%.$

If you sell the bond $4$ years after buying it$,$ and the bond's yield has changed to $7\mathrm{.}5\%,$ what is your annual HPR$?$

What sale price would have been required in order for the investor to have earned a $12\%$ annual HPR$?$

What YTM would be required for the bond to have the sale price you found in the previous question?