# Accounting Principles and the Mathematics behind them

In the last week or so, I have posted a few articles relating to a mathematical challenge and how to get the correct answer. One of the concepts needed for the challenge was a number line. Number lines help explain what happens when adding to or subtracting from a negative number. They also make Accounting simple.

If you want to read the original articles, here they are:

Disclaimer: I am not an Accountant and have never had any formal Accounting training.

I need to take you back to before I worked with Microsoft Dynamics GP, to my first commercial role as an employee. I was still studying engineering and had had my own software development business for a number of years. My maths knowledge was good but I had never done any Accounting.

The company I was working for purchased an open source accounting system called SBT, which was written in dBase and could be customised. Part of my role involved customising the system as well as making sure the accounting data was correct. I needed to learn accounting fast and so my brother, who was a Chartered Accountant at the time, gave me a quick lesson which has helped me to the present day.

Below is the summary of how to understand accounting principles from a purely mathematical perspective:

The main two reports for running a business are the Balance Sheet (which is a permanent record) and the Profit and Loss Statement (which resets each financial year). Those two reports in their simplest forms are governed by the following formulas:

• Balance Sheet: A = E + L : Assets = Equity + Liabilities
• Profit and Loss: P = I – X : Profit = Income – eXpenses

Debits and Credits are from the bank’s point of view and so are the opposite of what you expect when it comes to the maths involved. Yeah, I know it is backwards, but that is just the way it is, deal with it. 🙂

• Debits are positive
• Credits are negative

The different types of accounts on the reports have a usual balance that is either a Debit or Credit balance:

• Assets and Expenses are Debit Accounts and have a positive balance
• Liabilities and Income are Credit Accounts and have a negative balance

Now I can explain how number lines make accounting easy, just treat debits and credits as positive and negative numbers, respectively.

Debit balance accounts are positive.

• If I Debit (add to) a Debit account it gets more positive and has a larger value
• If I Credit (subtract from) a Debit account, it gets less positive and has a smaller value

Credit balance accounts are negative.

• If I Debit (add to) a Credit account, it gets less negative and has a smaller value
• If I Credit (subtract from) a Credit account, it gets more negative and has a larger value

Let’s try a Practical Example:

I have \$100 cash in the bank and I purchase a consumable item (Expense) for \$10 from a supplier on account. Here are the values of the accounts before any transactions.

 Account Name Account Type Account Value Bank Account Asset \$100 Accounts Payable Liability \$0 Expense Expense \$0

There are two transactions (journals) that will occur. The first when I pick up the item and using my account with the supplier to pay for it.

 Account Name Debit Credit Bank Account Accounts Payable \$10 Expense \$10

Then the second transaction occurs when I pay the account with cash from the bank.

 Account Name Debit Credit Bank Account \$10 Accounts Payable \$10 Expense

So now what’s the maths involved (with mathematical terms and values shown in red):

Here are the values of the accounts before any transactions.

 Account Name Account Type Account Value Bank Account Asset (Debit/Positive) \$100  +\$100 Accounts Payable Liability (Credit/Negative) \$0      -\$0 Expense Expense (Debit/Positive) \$0      +\$0

The first transaction in mathematical terms.

 Account Name Debit (Positive) Credit (Negative) Bank Account Accounts Payable \$10    -\$10 Expense \$10    +\$10

Here are the Account Values after the first transaction.

 Note that Accounts Payable is a Credit Balance account so it is normally negative, so the negative Maths value is shown as positive on the reports.

 Account Name Maths Value Accounting Value Bank Account +\$100 \$100 Accounts Payable -\$0 -\$10 = -\$10 \$10 Expense +\$0 +\$10 = +\$10 \$10

The second transaction in mathematical terms.

 Account Name Debit (Positive) Credit (Negative) Bank Account \$10    -\$10 Accounts Payable \$10    +\$10 Expense

Here are the Account Values after the second transaction.

 Account Name Maths Value Accounting Value Bank Account +\$100 -\$10 = +\$90 \$90 Accounts Payable -\$10 +\$10 = -\$0 \$0 Expense +\$10 \$10

So the final account values back in accounting terms are below:

 Account Name Account Type Account Value Bank Account Asset \$90 Accounts Payable Liability \$0 Expense Expense \$10

I know that the accountants reading this article will hate the way I have simplified everything, but this helped the engineer/mathematician in me understand the terminology and calculations involved.

What do you think?

David

PS: Stay tuned for another poll on a new mathematical puzzle.

This article was originally posted on http://www.winthropdc.com/blog.

18-Feb-2016: Fixed Typos and added comment about Accounts Payable being a Credit Account.

## 4 thoughts on “Accounting Principles and the Mathematics behind them”

1. Hi David,
Beautifully explained.
Below is my ‘Three’ ‘GOLDEN’ principal in Accounts.
1) Real
2) Personal
3) Nominal

1) Real
In Real – What you can feel, touch. It has included
e.g. Cash, furniture, Machinery etc whichever you can touch and feel.

Rule:
‘Debit’ what comes in & ‘Credit’ what goes out.

Accounting Transactions:
Purchase Furniture in Cash \$1000.00
So, we found two Real Accounts – 1) Furniture & 2) Cash
As per Rule:
Furniture A/c Dr \$1000
Cash A/c \$1000

2) Personal
In Personal A/c – A person, company, Group of Persons etc.

Rule:
‘Debit’ the Receiver & Credit the Giver

Example:
Mr. Joe give \$1000 to buy Furniture.
So two Accounts are in above transactions : 1) Real – i.e. Furniture A/c & Other is person i.e. Joe A/c

Accounting Entry will be :
Furniture A/c Dr. \$ 1000
To Joe A/c \$1000
Definitely business need to pay back to Joe even though it is as ‘Loan’ or as ‘Capital’.

3) Nominal
Rule: Debit all Expenses & Losses and Credit all Income & Gains.

So if your business has Expenses like Rent payment then you have to make it Debit Rent A/c. if you received Interest from Bank then you will credit ‘Interest A/c’ because it is Income.
e.g.
Rent Payment \$1000 ( Can you guess which two accounts are in this transaction any guess (Read first rule).
1) Cash A/c & 2) Rent A/c
Cash is Real it is gone out of business then I will pass entry ‘ Cash as Credit ‘ Rent as Expenses I will make Rent A/c as Debit.
Entry will be : Rent A/c Dr \$1000
Cash A/c \$1000

All transactions are in ‘Real, Personal & Nominal’ Accounts.
Other important – When you are doing Accounting you must think as Business instead of Individual. Think what comes in your business or what Expenses is for business, not as Individual.

Thanks Much

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2. David,

In the section labeled “Here are the Account Values after the first transaction,” the sum of the Accounting Value is \$120. Shouldn’t the Accounts Payable Accounting Value be -\$10 so that the sum is \$100?

Regards,

Steve Erbach
Appleton, WI

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• Hi Steve

Accounts Payable is a credit account, which means that in mathematic terms it has values that are negative on the number line.

However, you still refer to the accounting value as \$10, not -\$10.

I understand what you are saying and if I had another column, I would put the value in the credit column.

I believe it is correct as I have it.

Thanks

David

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