Suppose that:

The interest rate on a one$-$year bond today is $6\%$;

The interest rate on a one$-$year bond starting one year from now is expected to be $4\%$ per year;

The interest rate on a one$-$year bond starting two years from now is expected to be $3\%$ per year;

The risk premium on a two$-$year bond is $0\mathrm{.}5\%$; and

The risk premium on a three$-$year bond is $1\mathrm{.}0\%.$

Use that information to answer the following questions.

a$.$ According to the expectations theory, what is the interest rate today on a two$-$year bond? $6\mathrm{.}33\%($enter your response rounded to two decimal places$).$