Part 1:

If today (January 1st) the platinum spot price is $1,604 per ounce, what is the no-arbitrage futures price (per ounce) of platinum?

Part 2:

Suppose that on January 1st, the actual futures price for platinum was sufficiently close to the no-arbitrage price and you decided to enter short 8 platinum futures contracts. If today is July 1st, and if the platinum spot price today is 1,523.8, what is the value of the 8 platinum contracts?

Please show work so I am able to learn and follow!

Thank you!

You own a small Jewlery boutique and use precious metals in your production. To maintain a relatively stable Inventory of precious metals you trade regularly in the futures market. Today is January 1st and you noticed that your inventory of platinum is too high compared to the demand of platinum Jewelry for the year ahead. You are about to enter short in 8 platinum futures contract with delivery in September. Suppose storage costs for platinum are fixed at $20 per ounce and paid at the end of each quarter (March, June, September, December). Suppose further that the risk-free rate is 2.6% for all maturities (continuously compounded). The platinum futures contract has a size of 50 ounces