Question

This is a financial question from (options, futures and other derivatives book from c.  john hull.The price of gold is currently $500 per ounce. The forward price for delivery in one year is $700.An arbitrageur can borrow money at 10% per annum. What should the arbitrageur do? Assumethat the cost of storing gold is zero and that gold provides no income.

Accepted Answer

It seems clear to me that this person should borrow money to buy gold.  The person should make contracts to deliver the gold at the forward price in one year.  Then the person can hold the gold and deliver next year and make money.
To buy one ounce of gold now, the person needs $500.  If they borrow the entire sum and pay the interest rate you mention, their total cost for the ounce of gold will be $550.  You say that there is no storage cost and so their total cost for the gold is $550.
If you can buy for $550 and sell for $700, you should do it -- borrow as much as you can and buy as much gold as you can.

Answer

If the arbitrageur borrows money and buys gold now at $500 per ounce, and simultaneously enters into contract to sell gold at $700, he or she will get a sum of $700 per ounce after one year.
Out of this $700 received per ounce, a sum of $550 will be used for returning the principal amount of loan ($500) plus interest ($50) at the rate of 10% per annum.
This will still leave a surplus profit of $150 per ounce.
Therefore the arbitrageur should buy gold now and simultaneously enter into contract to sell gold for delivery in one year.

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