The real risk$-$free rate is $3\mathrm{.}05\%,$ inflation is expected to be $2\mathrm{.}75\%$ this year, and the maturity risk premium is zero. Ignoring any cross$-$product terms, what is the equilibrium rate of return on a $1-$year Treasury bond?

Suppose the real risk$-$free rate is $3\mathrm{.}00\%,$ the average expected future inflation rate is $2\mathrm{.}25\%,$ and a maturity risk premium of $0\mathrm{.}10\%$ per year to maturity applies, i$.$e$.,$ MRP $($or MP$)=0\mathrm{.}10\%(t),$ where $t$ is the number of years to maturity. What rate of return would you expect on a $1-$year Treasury security, assuming the pure expectations theory is NOT valid? Disregard cross$-$product terms, i$.$e$,$ if averaging is required, use the arithmetic average.

$1-$yearT$-$bond yields $5\mathrm{.}0\%$ and a $2-$year T$-$bond yields $7\mathrm{.}0\%.$ Assuming the pure expectations theory is correct, what is the market's forecast for $1-$year rates $1$ year from now?