The XXX company bought a June gold futures contract at $1,849.20 on May 10 , 2023 and deposited an initial margin of $12,600. The XXX company decided to keep this contract till delivery. The maturity of the gold futures contract is the third last business day of the contract month which is June 28, 2023 for the June 2023 gold futures contact and the contract size is 100 troy ounces. The maintenance margin is $7,200. The margin account is cleared by the brokerage firm if no positions are taken. The day-count convention is actual/actual.

a. Suppose the interest rate is 1.25%, the storage cost is 0.14% and the conveniency yield is 0.125%, what was the spot gold futures price on May 10, 2023?

b. If the gold futures settlement price was $1,851.58 on May 11, 2023, what amount was in the XXX margin account on May 11, 2022?

c. If the gold futures settlement price was $1848.82 on May 12, 2023, what amount was in the XXX margin account on May 12, 2022?

d. If the gold futures settlement price was $1894.23 on May 13, 2023, what amount was in the XXX margin account on May 13, 2023?

e. If the gold futures settlement price was $1792.35 on May 16, 2023, what was the amount was in the margin account?

f. If the gold futures settlement price is $1,849.20 on the June 28, 2023, how much is profit or loss in the XXX gold futures contract.