Suppose the $1-$year spot rate is $0\mathrm{.}8\%,$ and that a $2-$year $1\mathrm{.}5\%$ annual coupon, a $3-$year $2\%$ annual coupon bonds are trading at par $($$$100).$

Calibrate a $2-$year binomial interest rate model, assuming that interest rate volatility

is $10\%.$ What is the lowest rate at t$=2?$

Assume annual compounding. Round your answer to $4$ decimal places. For example if your answer is $3\mathrm{.}205\%,$ then please write down $0\mathrm{.}0321.$