The current spot price of gold is $1235 per ounce. CME futures contracts are 100 ounces each. The risk-free rate is 0.8%. The October contract (T=8 months) is currently $1245. Storage costs are $2 per ounce for 8 months (paid at the end of the 8 months). What is the theoretical futures price? If the futures price is $1290, is there an arbitrage trade? What about $1180?

Reference: Lecture notes

Storage costs can be viewed as negative income: F0 <= S0 e^((r+u)T) where u is the storage cost per unit time as a percent of the asset value. Alternatively, F0 = (S0+U)e^(rT) where U is the present value of the storage costs.