Situation

Imagine that you expect interest rates to increase and purchase a put option on Treasury bond $($T$-$bond$)$ futures. Assume the exercise price on T$-$bond futures is $$97,000,$ and the premium paid for the put option is $$3,000.$ Assume that interest rates do increase, and as a result, the price of the T$-$bond futures contract declines over time and is valued at $$89,000$ shortly before the option$$s expiration date. At this time, you decide to exercise the option and close out the position.

Requirements $($please respond in the same order requested and indicate each question's number$)$:

Is there any economic value in the option? Calculate it$,$ show the formula, do the math, and explain.

Is the option in the money, at the money, or out of the money? Explain.

Will you exercise the option? Explain.

In case you exercise the option, $($i$)$what would the net profit be$?$ Calculate it$,$ show the formula, do the math, and explain.

In case you do not exercise the option, what would the net profit be$?$ Calculate it$,$ show the formula do the math, and explain.