Cathy B. answered • 05/31/19

Experienced Accounting Tutor

In the original equation, which is often called the basic accounting equation, Assets = Liabilities + Equity.

These three variables can be re-arranged to solve for each variable as follows:

Assets = Liabilities + Equity

Liabilities = Equity - Assets

Equity = Assets - Liabilities

All three of these are permanent accounts; they aren't closed at month or period end. They will be reported at period end on the balance sheet as of a specific date in time.

Ending Equity in the above formula incorporates several temporary accounts that are closed to it prior at period end. We can expand Ending Equity or Equity as follows:

Ending Equity = (Beginning Equity + Income - Expenses + Owner Contributions - Owner Withdrawals)

Mathematically, we now have two different types of variables in this formula: permanent and temporary ones. Therefore, we would need to incorporate parentheses around the computation of temporary accounts values. Once we solve for ending equity, we again only have permanent accounts and the formula can be manipulated to solve for any of the three variables.

Simple proof:

Assets = 100

Liabilities = 50

Beginning Equity = 1

Income = 74

Expenses = 25

Ending Equity = 1 + 74 - 25 = 50

Assets = Liabilities + Equity (ending)

100= 50+ 50

Assets = Liabilities + (beginning equity + income - expenses) <-- Note that Ending equity isn't explicitly present; it's the sum of the parenthetical components

100 = 50 + 1 + 74 - 25