Suppose you and other investors expect that inflation will be $3\%$ next year, to rise to $5\%$ during the following year, and then to remain at $6\mathrm{.}4\%$ thereafter. Further you expect that the real risk free rate of interest will remain at $2\%$ and the maturity risk premium on treasury securities will rise from $\mathrm{.}2\%$ for one year bonds. Maturity risk premiums are expected to increase $0\mathrm{.}2\%$ for each year to maturity up to a limit of $1\mathrm{.}0$ percentage point on $5-$year or longer term T$-$bonds.

What is the return on a $4-$year bond? Write your answer as a percentage i$.$e$.8$ is $8\%.$