Quantitative Problem:

Today, interest rates on $1-$year T$-$bonds yield $1\mathrm{.}2\%,$ interest rates on $2-$year T$-$bonds yield $2\mathrm{.}5\%,$ and interest rates on $3-$year T$-$bonds yield $3\mathrm{.}7\%.$

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.

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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.

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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.

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