A $5-$year Treasury bond has a $3\mathrm{.}4\%$ yield. A $10-$year Treasury bond yields $6\mathrm{.}1\%,$ and a $10-$year corporate bond yields $8\mathrm{.}7\%.$ The market expects that inflation will average $3\mathrm{.}9\%$ over the next $10$ years $(($:$I{P}_{10}=3\mathrm{.}9\%$