Suppose the interest rate on a $1-$year T$-$bond is $4\mathrm{.}30\%$ and that on a $2-$year T$-$bond is $5\mathrm{.}90\%.$ Assuming the pure expectations theory is correct, what is the market's forecast for $1-$year rates $1$ year from now? Do not round your intermediate calculations. Round your final answer to $2$ decimal places.

a$.5\mathrm{.}10\%$

b$.7\mathrm{.}52\%$

c$.5\mathrm{.}86\%$

d$.4\mathrm{.}82\%$

$$ e$.7\mathrm{.}85\%$