There are three states of the world (1, 2, 3) for investors at t = 2.

Asset 1 pays $3 in state 1 and $4 in state 2.

Asset 2 pays $2 in state 1 and $1 in state 3.

Asset 3 pays $2 in state 1 and $2 in state 3.

Assets 1, 2, 3 are traded at $2.7 and $1.2 and $1.4 respectively.

(a) Find the price of a security that pays $1 at t = 2 regardless of the state of the world.

(b) Use your answer to part (a) to find the interest rate of a risk-free two-year zero coupon bond.