Digital payoff outside the 15 to 20 band

A contract pays $1$ at expiry if the stock finishes at or below $15$ or at or above $20$, and $0$ otherwise. Digital calls (paying $1$ if $S_T\ge K$) are quoted at: strike $15$ for $0.73$, strike $17.5$ for $0.34$, strike $20$ for $0.13$. The discount factor to expiry is $0.9$. What is the contract worth today?

$0.30$. The contract is a digital call at $20$ plus a digital put at $15$. A digital put and digital call at the same strike add up to a bond, so the put costs $0.9-0.73=0.17$, and the total is $0.13+0.17=0.30$ (ignoring the measure-zero point $S_T=15$).