Upper bound on forward settlement price

let's see if there's a way to make a risk-free profit and let me just tell you right from the get-go there's usually not many ways to make a risk-free profit in the world so this is very theoretical if the spot price for gold was $1000 so the spot price literally just means the market price if you were to buy or sell gold today and actually exchange hands then you would pay or sell the gold for $1000 per ounce and let's also say that the 1-year forward settlement price is $1200 per ounce so if you want to buy gold one year from now you can agree right now to buy it for $1,200 or if you want to sell gold one year from now you can agree right now to sell it for $1,200 buy entry into a forward or futures contract and just the other details the interest rate to borrow money is 10% and the carrying cost of gold is $50 per ounce per year and the carrying cost means if I had an ounce of gold and I wanted to hold it responsibly I wanted to store it maybe someplace in a safe at a bank and I wanted to insure it in case it got stolen or in case someone lost it that would cost me $50 per ounce per year so that's what we mean by carrying cost now let's say you could also invest money risk-free in this type of a market I've just made up these numbers for 5% a year so how could you make the money well you could and we're assuming you start with nothing so you could literally just borrow you could borrow $1,000 you borrow $1,000 and then you use that to buy an ounce of gold in the spot market so you buy you buy one ounce of gold and you also agree to sell it in the future so you also agree agree so you enter to that forward contracts let me just write this way enter into forward into forward as the seller as the seller so you are on the spot market you are the buyer and on the forward market one year from now you agree to be the seller so let's just think about how this is going to play out so over the course of the year you will have some cost you have to pay the interest on this thousand dollars that's 10% so you're gonna have to pay $100 in interest and you're going to have to pay the carrying cost $50 per ounce so $50 carrying cost carrying cost and so when we end up a year from now you can sell you will sell the gold so sell you will sell the gold for for $1,200 for $1,200 one year from now and you know you can do that because you entered into the forward agreement and then you can pay back pay pay back the thousand dollars the thousand dollar loan plus $100 interest plus $100 interest and let's say you have to pay the carrying cost at the end of the year to the bank so plus the $50 carrying cost so how much did we how much did we profit well we get $1,200 and we had to pay back 1150 so we make so 1200 minus a thousand minus 100 minus 50 we make a profit we make a profit of $50 so the big takeaway here is is that these type of things normally don't exist if they did people would do it all day and all night and this price would go up because everyone would want to buy on spot and this price would go down because everyone would want to sell in the futures market everyone would want to do this right here so the appropriate price is this one should not this price based on these numbers right here should not be any higher than 1150 so the correct market price here if if we didn't want a risk-free profit or essentially what the arbitrage errors would make happen by by kind of taking advantage of this it would eventually go to 1150 so it's essentially the spot price plus the cost to borrow money at that spot price plus plus the carrying cost so that's essentially what would be the rational price for the futures contract or the forward settlement price