Inflation Risk Premiums

Because of a recession, the inflation rate expected for the coming year is only $5\%.$ However, the inflation rate in Year $2$ and thereafter is expected to be constant at some level above $5\%.$ Assume that the real risk$-$free rate is r$*=2\%$ for all maturities and that there are no maturity risk premiums. If $3-$year Treasury notes yield $2$ percentage points more than $1-$year notes, what inflation rate is expected after Year $1?$ Round your answer to the nearest whole number.

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