Suppose the interest rate on a $1-$year T$-$bond is $4\mathrm{.}90\%$ and that on a $2-$year T$-$bond is $5\mathrm{.}80\%.$ Assume that the pure expectations theory is NOT valid, and the MRP is zero for a $1-$year T$-$bond but $0\mathrm{.}40\%$ for a $2-$year bond. What is the yield on a $1-$year T$-$bond expected to be one year from now? Do not round your intermediate calculations. Round your final answer to $2$ decimal places.

a$.5\mathrm{.}15\%$

b$.6\mathrm{.}71\%$

c$.5\mathrm{.}44\%$

d$.5\mathrm{.}90\%$

e$.5\mathrm{.}39\%$