Suppose the interest rate on a $1-$year T$-$bond is $5\mathrm{.}40\%$ and that on a $2-$year T$-$bond is $6\mathrm{.}70\%.$ 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$.6\mathrm{.}27\%$

b$.6\mathrm{.}10\%$

c$.7\mathrm{.}21\%$

d$.8\mathrm{.}02\%$

e$.5\mathrm{.}85\%$