Example 5.2a, An Introduction to Mathematical Finance, Sheldon Ross: Let S be the present market price of a specified stock. In a forwards agreement, one agrees at time 0 to pay the amount F at time t for one share of the stock that will be delivered at the time of payment. That is, one contracts a price for the stock, which is to be delivered and paid for at time t.

We will now present an arbitrage argument to show that if interest is continuously discounted at the nominal interest rate r, then in order for there to be no arbitrage opportunity we must have F = S e^rt

To see why this equality must hold, suppose first that instead F < Se^rt. In this case, a sure win is obtained by selling the stock at time 0 with the understanding that you will buy it back at time t. Put the sale proceeds S into a bond that matures at time t and, in addition, buy a forwards contract for delivery of one share of the stock at time t. Thus, at time tt you will receive SertSert from your bond. From this, you pay FF to obtain one share of the stock, which you then return to settle your obligation. You thus end with a positive profit of Se^rt F.

On the other hand, if F > Se^rt, then you can guarantee a profit of FSe^rt by simultaneously selling a forwards contract and borrowing S to purchase the stock. At time tt you will receive F for your stock, out of which you repay your loan amount of Se^rt

Everything makes sense in the above para, except that why haven't we included the price of the forward contract into the picture as well? The forward contract that we are buying would have some price attached to it right? And that price for buying the contract should make a difference to our returns. Nobody will see a forward contract for free, right?