Disposable income is your income left to save and spend after paying taxes.
Discretionary income is the amount of income left after essentials are taken care of, such as food and shelter. http://www.investorwords.com/1483/discretionary_income.html
I am not familiar with a specific term referring to income after ALL bills are paid, but I think the term you are looking for is discretionary income.
No, the accounting term is "Net Income". To be more exact, on the Income Statment, you have Revenue (or Sales) and you deduct Cost of Goods Sold from that to get the Gross Profit, you then decuct your Operating Expenses and would then get "Operating Income"
After that you deduct Interest Expense & Income Tax Expense and you get Net Income. If you pay Dividends, then what is left is "Retained Earnings". If you do not pay Dividends, then your Net Income is the same as your Retained Earnings.
Hope that helps
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