say you have an IBM call option whose current price is 100$. The time to maturity is 3 month.

So S=100$

t has different notations.

T usually denotes the time of expiration of the option

0 or t is used to refer to the current time. In this case, if you take 0 as the coronet time, T=0.25 yr, while if you take t as the current time, T-t=0.25.

It is the time to maturity that affect the option's price.