How Does the Concept of “Implied Interest Rate” Arise from the Futures Price?

The implied interest rate arises directly from the cost of carry relationship. By observing the spot price, the futures price, and the time to expiration, an arbitrageur can solve the cost of carry formula for the interest rate.

This calculated rate is the "implied interest rate" or "implied repo rate." It represents the theoretical interest rate required to justify the observed futures price, assuming no other costs.