How Does the Time Value of Money Concept Underpin the Risk-Free Rate’s Inclusion?

The time value of money (TVM) principle states that a dollar today is worth more than a dollar tomorrow. The risk-free rate in the Black-Scholes model accounts for this by discounting the strike price back to the present value.

This acknowledges that the option buyer does not have to pay the strike price until expiration, allowing them to earn the risk-free return on that capital in the interim.