max(S - K, 0) for a call. Option price = intrinsic value + time value, and time value is strictly positive before expiry.
That is the whole argument for never exercising an American call on a non-dividend stock early: exercising captures only intrinsic value and discards the time value, so selling the option always yields more.
Time value is largest at the money and decays to zero at expiry, at an accelerating rate - see theta.