Suppose the interest rate on a $1-$year T$-$bond is $5\mathrm{.}10\%$ and that on a $2-$year T$-$bond is $6\mathrm{.}50\%.$ 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$.7\mathrm{.}92\%$

b$.5\mathrm{.}60\%$

c$.6\mathrm{.}07\%$

d$.7\mathrm{.}11\%$

e$.5\mathrm{.}74\%$