The yield curve for default$-$free zero$-$coupon bonds is currently as follows:

Maturity $($years$)$ YTM

$111\mathrm{.}0\%$

$212\mathrm{.}0$

$313\mathrm{.}0$

Required:

a$.$ What are the implied one$-$year forward rates? $($Do not round intermediate calculations. Round your answers to $2$ decimal places.$)$

b$.$ Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will the pure yield curve $($that is$,$ the yields to maturity on one$-$ and two$-$year zero$-$coupon bonds$)$ be next year?

multiple choice

There will be a shift upwards in next year's curve.

There will be a shift downwards in next year's curve.

There will be no change in next year's curve.

c$.$ What will be the yield to maturity on two$-$year zeros? $($Do not round intermediate calculations. Round your answers to $2$ decimal places.$)$

d$.$ If you purchase a two$-$year zero$-$coupon bond now, what is the expected total rate of return over the next year? $($Hint: Compute the current and expected future prices.$)$ Ignore taxes. $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

e$.$ If you purchase a three$-$year zero$-$coupon bond now, what is the expected total rate of return over the next year? $($Hint: Compute the current and expected future prices.$)$ Ignore taxes. $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$