# Can someone explain to me the intuition behind the discount factor for this simple payoff? [closed]

Let's say you enter into a contract today in which in time t, you receive the difference between the underlying stock price and 100. Denote the stock price as S. Why is today's value of such a contract equal to:

S - 100 * exp(-rt)

As opposed to:

(S - 100) * exp(-rt)

I see the former in texts a lot.

Thanks!

$$S_t-100$$
The present value of the stock is $$S_0$$, it’s current price; and the present value of 100 is its discounted value as you correctly explained in your question.