Quantitative Problem:

Today, interest rates on $1-$year T$-$bonds yield $1\mathrm{.}5\%,$ interest rates on $2-$year T$-$bonds yield $2\mathrm{.}1\%,$ and interest rates on $3-$year T$-$bonds yield $3\mathrm{.}6\%.$

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.

$\%$

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.