Problem 220 of 333MediumFinanceP220

Two-period bond on a rate tree

The one-period interest rate is $4\%$ today. Next period it will be $6\%$ or $2\%$ , each with risk-neutral probability $\tfrac12$ . Price a zero-coupon bond that pays $100 at time 2, find its two-period yield, and compare the price with the same bond if the rate were known to stay at $4\%$ . Which is higher, and why?
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