Suppose you see the following prices:

a. 1-year $100 zero coupon bond selling for $86.70

b. 3-year 10% coupon $1,000 par bond selling for $963

c. 2-year 10% coupon $1,000 par bond selling for $941

Assume that the pure expectations theory for the term structure of interest rates holds, no liquidity or term premiums exists, and the bonds are equally risky. What is the implied 1-year rate two years from now?