Today, interest rates on $1-$year T$-$bonds yield $1\mathrm{.}2\%,$ interest rates on $2-$year T$-$bonds yield $2\%,$ and interest rates on $3-$year T$-$bonds yield $3\mathrm{.}3\%.$

a$.$ If the pure expectations theory is correct, what is the yield on $1-$year T$-$bonds one year from now? Be sure to use a geometric average in your calculations. Do not round intermediate calculations. Round your answer to four decimal places.

$2\mathrm{.}8063\%.$ b$.$ If the pure expectations theory is correct, what is the yield on $2-$year T$-$bonds one year from now? Be sure to use a geometric average in your calculations. Do not round intermediate calculations. Round your answer to four decimal places. $\_\_\_\_\_\_\_\_\_\_\_\_\%.$ c$.$ If the pure expectations theory is correct, what is the yield on $1-$year T$-$bonds two years from now? Be sure to use a geometric average in your calculations. Do not round intermediate calculations. Round your answer to four decimal places. $\_\_\_\_\_\_\_\_\_\_\%$