Suppose the interest rate on a $1-$year government bond is $3\mathrm{.}00\%,$ on a $4-$year government bond is $3\mathrm{.}50\%$ and that on a $6-$year government bond is $4\mathrm{.}90\%.$ What is the market's forecast for $2-$year rates $4$ years from now, assuming the pure expectations theory is correct? Show your work.