Using a BA Calculator, show all workings

Question :

a) 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?