# Accounting - Mathematical Concepts used

Accounting is built on mathematical concepts. The early development of accounting involved mathematicians.

The first printed treatise of bookkeeping in the world is the "Summa de Arithmetica, Geometria, Proportioni et Proportionalita" written by Luca Pacioli. The treatise was published in Venice in 1494, and was reprinted at Toscolano in 1523. This work is one of the most important books on mathematics and has had an enormous impact on the field of accounting ever since.

• ## Numerals and Literals

Numerals are numbers. Literals are alphabets used in place of (or to represent) numbers.

• ## Constants, Variables, Unknowns

Constants are those which have a fixed value. Variables are those which are capable of having more than one value. When the value represented by the constant is not known we call it an unknown.

Numerals are always constants whereas literals can be either constants or variables.

• ## Terms

Constants and variables combined together with the mathematical operations of multiplication (×) and division (÷) form terms.

• ## Expression

Terms combined together using the mathematical operations of addition (+) and subtraction (−) form an expression.

• # Equation

In mathematics, an equation is a statement of equality between two expressions.

Expression1 = Expression2

# The Fundamental Accounting Equation

The total idea of accounting is built around a mathematical equation called the Fundamental Accounting Equation.

# Capital + Liabilities = Assets

It is a statement of equality between two expressions, one representing assets and the other representing liabilities. As per this equation, the value of the assets of an organisation should always be equal to the value of its liabilities.

# Isn't it Liabilities = Assets?

Yes, the fundamental accounting equation in its true sense should be Liabilities = Assets. This realtion is even true.

The explanation for the equation being written as Capital + Liabilities = Assets lies in the separate entity concept. Since the owner is also an alien to the business, the amount that is contributed by the owner towards his capital should also be treated as a liability to the business. But since it is of a special nature and it is a liability which differs from the others in the sense that it takes the maximum amount of risk in the business, it would be appropriate to show it distinctly always.

Therefore the liabilities on the LHS of the accounting equation are divided into two as capital and liabilities.

# Total Liabilities = Total Capital Employed = Owned Capital + Loaned Capital

The total capital employed in the business comes from two sources. One the ownership of the business (which we call owned capital) and two from non-owners as liabilities (which we call loaned capital).

Since the owner is also alien to business and the owner's contribution is to be treated as a liability we can say that total liabilities is equal to total capital.

# Mathematical Interpretation of the Accounting Equation

• ## Terms

Each element of accounting i.e. each account head forms a term.

Thus the accounting equation can be interpreted as

__ a/c + ___ a/c + ___ a/c = ___ a/c + ___ a/c

• ## Expression

Each of Capital, Liabilities and Assets will form an expression with each of its constitutent elements forming a Term.

• # Equation

The fundamental accounting equatiion itself is a mathematical equation.

# What are Assets?

Since this is the initial stages of learning accountancy, it would be better to have a simple understanding on what an asset is.

# Asset

• Anything of material value or usefulness that is owned by a person or organisation
• something useful or valuable
• something that can be liquidated by converting to cash or another asset
• wealth
• holding
• liability

Entities which are capable of being liquidated/realised by forfeiting their possession are called assets.

## examples

• Motor Car, Buildings, Land, Furniture etc.
• Debtors (those who owe us money).

They clear off their dues by paying cash, which can be interpreted as liquidation of debtors.

• Goodwill.

It can be sold and realised in cash at the time of sale of business.

# Liquidate

• convert to cash

Liquidation with respect to assets is the process of converting the asset to cash by handing over its possession.

The faster an asset is capable of being converted to cash, the more liquid it is.

• Cash is the highest liquid asset.

It needs no time to get converted to cash.

• Goodwill of an organisation or a business is the least liquid asset.

It exists as long as the organisation exists and can only be realised only on shutting down or selling away the business.