An investor plans to buy five consecutive $1-$year T$-$bills over a five$-$year period. The current interest rate of a $1-$year T$-$bill is $4\mathrm{.}0\%,$ the expected interest rate one year from now for a $1-$year T$-$bill is $3\mathrm{.}5\%,$ the expected interest rate two years from now for a $1-$year T$-$bill is $3\mathrm{.}0\%,$ the expected interest rate three years from now for a $1-$year T$-$bill is $2\mathrm{.}5\%,$ and the expected interest rate four years from now for a $1-$year T$-$bill is $2\mathrm{.}5\%.$

Based on Expectations Theory, what is the expected interest rate of a $5-$year T$-$note?