At your favorite bond store, Bonds-R-Us, you see the following prices: a. 1-year $1000 zero selling for $950 b. 3-year 5

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At your favorite bond store, Bonds-R-Us, you see the following
prices:
a. 1-year $1000 zero selling for $950
b. 3-year 5% coupon $1000 par bond selling for $1000
c. 2-year 4% coupon $1000 par bond selling for $1000
Assume that the pure expectations theory for the term structure
of interest rates holds, no liquidity or maturity premium exists,
and the bonds are equally risky. What is the implied 1-year rate
two years from now?