How Is a Box Spread Used to Calculate Implied Interest Rates in the Options Market?

Since the theoretical profit of a box spread is equal to the difference between the two strike prices, discounted at the risk-free rate, the price of the box spread itself can be used to back-solve for the implied risk-free interest rate. If the market price of the box spread is known, the interest rate that makes the present value of the payoff equal to the current cost is the implied interest rate for the period until expiration.