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I a new to finance math so I am confused on how to answer this. I understand the concept of an arbitrage opportunity. The way I understand it is when after you close your position you make a profit. A profit which is made through inconsistencies in the market.

But how do I describe an arbitrage opportunity mathematically? For example:

The price of oil is currently 100 dollars per barrel. The contract size is one barrel. The forward price for delivery in one year is 130 dollars. You can borrow money at 7% per annum with annual compounding. Assume the cost of storing one barrel of oil is nothing nor does it provide any income.

How can I describe an arbitrage opportunity here? I don't know how to approach this...any help would be appreciated.

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    How much would you have to pay back if you borrow $100 today? How much will you make in a year when you pay it back? What would your profit/loss be? – 2017-02-06

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An arbitrage opportunity comes about because you can make a number of trades that make a profit regardless of future behavior. If you buy a barrel of oil now you have to borrow the money to do that. You then sell a forward contract to deliver that oil in one year. How much do you earn? You pay back the loan and you are back to having no assets or liabilities except the profit. How much is that?

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    So I'd use the formula $P(1=r)^t$ because it is not continuous compounding. If true, then I'd pay back 107 dollars – 2017-02-06
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    So the arbitrage opportunity is just an explanation of how much I can make in the deal? – 2017-02-06
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    Yes. You should explain the deal you would make and why it guarantees a profit. Under the assumption of no storage or delivery cost, you must have that the future price is no higher than the inflated spot price or there will be arbitrage. – 2017-02-06