On March $1,2025,$ Ferguson Corp. purchased a put option on shares of SST stock. The contract was for $100$ shares at a strike price of $$100$ per share, with an expiration date of May $31,2025.$ Ferguson settled the option on May $5($assume cash settlement$).$ Additional information pertaining to the option is provided below.

March $1$ March $31$ May $5$

Price of SST stock: $$100$ $$90$ $$95$

Time value of option: $$50$ $$40$ $$30$

Required:

$1.$ Compute the cost of the option paid by Ferguson Corp. on March $1,2025.$

$2.$ Compute the balance of the option account on date of settlement.