Suppose that the interest rate on a one$-$year bond is $7\%$ today and the interest rates expected on one$-$year bond in the future are $6\%$ in one year, $5\%$ in two years, and $4\%$ in three years.

$.$ According to the expectations theory of the term structure, what are the interest rates today on a two$-$year bond, a three$-$year bond, and a four$-$year bond?

$.$ Assume the term premium for an $n-$year bond, $tn.$ If the term premium is equal to $0\mathrm{.}5\%$ times the number of years to maturity of a bound $,$ when $($:$n2\}.$ For example, the term premium is $1\%(0\mathrm{.}5\%**2)$ for a two$-$year bond.

For times maturity of two, three and four years, what are the interest rates today on a two$-$year bond, a three$-$year bond and a four$-$year bond?