Suppose that a $1-$year zero$-$coupon bond with face value $$1000$ currently sells at $$943\mathrm{.}4,$ while a $2-$

year zero sells at $$849\mathrm{.}9.$

a$.$ What is the yield to maturity of the $2-$year zero?

b$.$ What is the implied short rate for the second year?

c$.$ Based on the above result, what should be the price of that $2-$year zero$-$coupon bond at the beginning of the

second year? If you hold this bond over the entire first year, how much should be your holding period return? d$.$ What would your HPR change if the actual $1-$year interest rate in year $2$ is higher than the expected short rate

calculated in part $($b$)?$