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The preferred journal entry would be a debit to Rent Expense and a credit to Cash. Office expense is usually used for office supplies. I would not recommend home office expense because for tax purposes it could be somewhat of a red flag.
Yes, if the corp doesn't have the cash at the time, you could record it to the officer loan and then when the corp gets the cash, pay it against the officer loan. It accomplishes the same thing but that way it is a two step process.
I'm not sure what you are asking about the expense report. Expense reports are usually used to reimburse an employee for actual expenses incurred in behalf of the company, not to accrue rents owed.