A trader owns gold as part of a long-term investment portfolio. The trader can buy gold for $1250 per ounce and sell gold for $1249 per ounce. The trader can borrow funds at 6% per year and invest funds at 5.5% per year. (Both interest rates are expressed with annual compounding. Do not use continuous compounding). For what range of one-year forward prices of gold does the trader have no arbitrage opportunities? Assume there is no bid–offer spread for forward prices.
Where did you get this question?
From my exercise
you can borrow money, buy gold, store it safely (this is not included), or lend it to a jewler (this is not included).
so, borrow 1250, buy gold sell forward. 12 months later repay 1325, so if forward is 1325 or above you can make a profit.
or, you can sell your gold for 1249, invest for 12 months, and collect 1317.695 if fwd rate is lower than that then you make a profit.
so simple answer is 1317.695-1325.
a quick google told me convenience yield is normally negative for gold, therefore you need to include the cost of the secure storage for the question to be answered properly.