If you sell the $2\mathrm{.}5\%$ bond in $4$ years at $$1000$ par after buying it$,$ it has a YTM of $8\mathrm{.}5\%,$ and the bond's yield has changed to $7\mathrm{.}5\%.$ What is your HPR$?$ Then what sale price would have been required in order for the investor to have earned a $12\%$ HPR$?$ After that, what YTM would be required for the bond to have the sale price you found in the previous question?