2.1 The Accounting Equation and Double Entry
- State the accounting equation and explain why it must always balance.
- Analyze a transaction by its effect on assets, liabilities, and owner's equity.
- Apply the rules of debits and credits and record a balanced journal entry.
- Post entries to the ledger and prove the books with a trial balance.
Every financial statement rests on a single identity: a firm's economic resources equal the claims against those resources, measured at the same instant. This section builds that identity from the ground up — why it can never fall out of balance, how the bookkeeper's own notation of debits and credits keeps it that way, how a transaction becomes a journal entry and then a posted ledger balance, and how the trial balance proves the books, transaction by transaction, to the end of the month.
At every instant, a firm's assets equal the claims of its creditors plus the claims of its owner:
$$ \text{Assets} = \text{Liabilities} + \text{Owner's Equity}. $$Because each transaction affects at least two accounts by equal and opposite amounts, the equation stays in balance — the principle of double entry.
The equation holds not because bookkeepers are careful, but because of how a transaction is defined. The left side lists what the firm controls; the right side lists who supplied the money for it — the same pool counted two ways, so the two sides move together. Take in a resource, and a matching claim appears with it. Give up a resource, and a claim is settled by the same amount. Shift value within one side, and the other side never moves. Post any transaction to both sides at once and the equation holds level, every time — equal and opposite, by construction, not by care.
Figure — Post a $2,500 transaction to both sides and the beam holds level — equal-and-opposite, every time.
A new café has just opened its books. Where does each item belong in the equation — asset, liability, or owner's equity? Cash in the till and the espresso machine the café owns; a bank loan the café must repay and an unpaid invoice from the coffee roaster; the owner's opening investment of $8,000.
Sort by asking who holds the claim. Cash and the espresso machine are resources the café controls — assets. The bank loan and the roaster's invoice are amounts owed to outsiders — liabilities. The owner's $8,000 investment is the owner's residual claim — owner's equity.
Recording that balance takes a notation of its own: the bookkeeper's two words, debit and credit.
Every account has two sides. A debit (Dr) is an entry on the left side; a credit (Cr) is an entry on the right. The words carry no sense of good or bad — they only say which side. For a transaction to be recorded, the debits must equal the credits:
$$ \sum \text{Debits} = \sum \text{Credits}. $$Which side increases an account depends on where it sits in the equation. Assets rise with debits; liabilities and equity rise with credits — mirror images across the equals sign.
asset — an economic resource the firm controls and expects to provide future benefit; increases with a debit.
liability — an obligation owed to an outside party; increases with a credit.
owner's equity — the owner's residual claim on assets once liabilities are settled; increases with a credit.
| Account type | Side of the equation | Increases with a | Normal balance |
|---|---|---|---|
| Assets | Left | Debit | Debit |
| Liabilities | Right | Credit | Credit |
| Owner's Capital (equity) | Right | Credit | Credit |
| Revenues (raise equity) | Right | Credit | Credit |
| Expenses & Drawings (lower equity) | Left | Debit | Debit |
An account's normal balance is the side that increases it. Assets and the things that reduce equity live on the left; liabilities, capital, and revenue live on the right.
The owner invests $10,000 of cash to open the business. Which accounts change, in which direction, and does the equation still hold?
Solution
Cash (an asset) increases by $10,000, so it is debited. Owner's Capital (equity) increases by $10,000, so it is credited. Two accounts move, by equal amounts, on opposite sides of the equation, which stays in balance: assets rise \(+\$10{,}000\), liabilities are unchanged, and owner's equity rises \(+\$10{,}000\).
An owner opens a consulting firm by depositing $25,000 of personal cash into the business bank account. Which two accounts change, in which direction, and does the equation still balance?
Answer
Cash (an asset) rises $25,000, so it is debited. Owner's Capital (equity) rises $25,000, so it is credited. Both sides of the equation move up by the same amount: assets \(+\$25{,}000\) = liabilities $0 + equity \(+\$25{,}000\) — the same shape as Example 2.1.1, at a different scale.
Put the two rules together and a transaction becomes a journal entry: name the accounts, decide which side each one moves on, and set the amounts so the columns tie out.
| Account | Debit | Credit |
|---|---|---|
| Cash (asset) | $10,000 | |
| Owner's Capital (equity) | $10,000 |
Post it: the debit lands on the left of the Cash account, the credit on the right of Owner's Capital. Debits equal credits, so the check line holds at $0.
Figure — Debit left, credit right — the two sides post together and the balance check never leaves $0.
The firm buys $600 of office supplies from a vendor and agrees to pay in 30 days. No cash changes hands today. Record the journal entry, and check that the equation holds.
Solution
Supplies (an asset) increases $600, so it is debited. Because the firm owes the vendor, Accounts Payable (a liability) increases $600, so it is credited. Debits equal credits, and the equation grows by $600 on each side:
| Account | Debit | Credit |
|---|---|---|
| Supplies (asset) | $600 | |
| Accounts Payable (liability) | $600 |
Assets \(+\$600\) = Liabilities \(+\$600\) + Equity $0. Buying on credit lifts an asset and a liability together — equity is untouched.
The firm buys a $1,800 laptop from a supplier, agreeing to pay the full amount next month. Write the journal entry, name the debit and the credit, and confirm the entry balances.
Answer
| Account | Debit | Credit |
|---|---|---|
| Equipment (asset) | $1,800 | |
| Accounts Payable (liability) | $1,800 |
Equipment (an asset) is debited $1,800; Accounts Payable (a liability) is credited $1,800 — the same shape as Example 2.1.3, an asset and a liability rising together. Debits $1,800 = credits $1,800, so the books stay in balance.
The firm buys $4,000 of equipment, paying $1,500 in cash and owing the $2,500 balance. Which accounts change, and does the equation still hold?
Solution
Equipment (an asset) rises $4,000; Cash (an asset) falls $1,500; Accounts Payable (a liability) rises $2,500. Assets change by \(+4000 - 1500 = +2500\), matched exactly by the \(+2500\) rise in liabilities — three accounts move, but the equation holds throughout.
Figure — Three accounts move, but Assets keeps equalling Liabilities + Equity throughout.
The firm pays $800 cash for this month's office rent. Rent is an expense — it uses up a resource without creating anything the firm keeps. Record it, and trace the effect on the equation.
Solution
| Account | Debit | Credit |
|---|---|---|
| Rent Expense (reduces equity) | $800 | |
| Cash (asset) | $800 |
Rent Expense is debited $800, because expenses sit on the left: they reduce equity, and a reduction to a credit-side balance is recorded on the opposite, debit side. Cash (an asset) is credited $800 as it leaves the firm. Assets fall \(\$800\) and equity falls \(\$800\) — the equation stays level, one step lower. An expense is recorded with a debit precisely because it lowers the owner's claim.
The firm pays $1,200 in cash for employee salaries this week. Write the journal entry, and state what happens to assets, liabilities, and equity.
Answer
| Account | Debit | Credit |
|---|---|---|
| Salaries Expense (reduces equity) | $1,200 | |
| Cash (asset) | $1,200 |
Salaries Expense is debited $1,200 (it reduces equity, so it increases on the left); Cash is credited $1,200 as it leaves. Assets \(-\$1{,}200\) = liabilities $0 + equity \(-\$1{,}200\) — every expense paid in cash follows this same debit-expense, credit-cash shape.
The firm completes a job and is paid $3,000 in cash on the spot. Revenue is earned. Record the entry, and show which way the equation moves.
Solution
| Account | Debit | Credit |
|---|---|---|
| Cash (asset) | $3,000 | |
| Service Revenue (raises equity) | $3,000 |
Cash (an asset) is debited $3,000 as it comes in; Service Revenue is credited $3,000, because revenue raises equity and so increases on the right. Assets and equity both rise $3,000 — the mirror image of paying an expense. Revenue is credited because it builds the owner's claim.
The firm finishes $2,000 of work and bills the customer, who will pay in 30 days. No cash arrives yet. Write the journal entry, and explain why revenue is still recorded now.
Answer
| Account | Debit | Credit |
|---|---|---|
| Accounts Receivable (asset) | $2,000 | |
| Service Revenue (raises equity) | $2,000 |
Accounts Receivable — an asset, the customer's promise to pay — is debited $2,000; Service Revenue is credited $2,000. Revenue is recorded when it is earned, not when cash is collected. Assets \(+\$2{,}000\) = liabilities $0 + equity \(+\$2{,}000\) — the debited asset is a receivable instead of cash, but equity still rises with the revenue.
Each journal line above was posted to its account in the ledger as it was recorded. Posting keeps a running balance: for Cash, an asset, the debits pile up on the left and payments net against them.
| Transaction | Debit | Credit | Balance |
|---|---|---|---|
| Owner's investment | $10,000 | $10,000 | |
| Buy equipment (cash portion) | $1,500 | $8,500 | |
| Services rendered for cash | $3,000 | $11,500 | |
| Pay rent for the month | $800 | $10,700 |
At the end of the month, every account's balance is listed together in a trial balance, to prove that debits and credits still agree.
| Account | Debit | Credit |
|---|---|---|
| Cash | $10,700 | |
| Equipment | $4,000 | |
| Accounts Payable | $2,500 | |
| Owner's Capital | $10,000 | |
| Service Revenue | $3,000 | |
| Rent Expense | $800 | |
| Totals | $15,500 | $15,500 |
The columns agree at $15,500.
A trial balance that ties out is necessary — but it only proves the debits and credits are equal, not that every account was chosen correctly. Ties are a check on arithmetic, not on judgment.
The debit and credit columns of this trial balance do not agree. Find the account placed on the wrong side, and give the corrected totals.
| Account | Debit | Credit |
|---|---|---|
| Cash | $10,400 | |
| Accounts Payable | $1,500 | |
| Owner's Capital | $6,000 | |
| Service Revenue | $2,900 | |
| Totals | $11,900 | $8,900 |
Answer
Accounts Payable is a liability — normal balance a credit — so its $1,500 belongs in the credit column. Move it there and both columns agree at $10,400. A figure on the wrong side offsets the balance by twice its amount: here the $3,000 gap is exactly \(2 \times \$1{,}500\).
Zoom out to the whole month, and the same four transactions still agree, column for column:
| Metric | Value |
|---|---|
| Total debits (Cash, Equipment, Rent Expense) | $15,500 |
| Total credits (Payable, Capital, Revenue) | $15,500 |
| Difference (debits less credits) | $0 |
| Ledger accounts touched | 6 |
The discipline is that the two columns agree — not that any single figure is large.
Trace the whole month, transaction by transaction: the owner invests cash, the firm buys equipment (part cash, part credit), earns service revenue in cash, then pays rent. What is the net effect on each part of the equation?
Solution
| Transaction | Δ Assets | Δ Liabilities | Δ Equity |
|---|---|---|---|
| Owner invests cash | +$10,000 | — | +$10,000 |
| Buy equipment (cash + credit) | +$2,500 | +$2,500 | — |
| Earn service revenue | +$3,000 | — | +$3,000 |
| Pay rent | −$800 | — | −$800 |
| Net change | +$14,700 | +$2,500 | +$12,200 |
Assets \(+\$14{,}700\) = Liabilities \(+\$2{,}500\) + Equity \(+\$12{,}200\) — every line kept the equation whole.
The owner withdraws $500 of cash from the business for personal use. This is a drawing, not an expense. Record it, and show the effect on the equation — does the business earn or lose anything?
Answer
| Account | Debit | Credit |
|---|---|---|
| Owner's Drawings | $500 | |
| Cash (asset) | $500 |
Owner's Drawings is debited $500 (drawings reduce equity, so they increase on the left); Cash is credited $500 as it leaves. The business earns nothing here — this is the owner pulling value back out. Assets \(-\$500\) = Liabilities $0 + Equity \(-\$500\): a draw lowers assets and equity together, like an expense on the equation, but it reflects the owner's choice, not the cost of earning revenue.
Every transaction, from the owner's first deposit to the owner's last draw, moves through the same five steps — the accounting cycle:
- Analyze — identify the accounts a transaction touches and the direction of each change.
- Journalize — record it as a balanced entry of debits and credits, in date order.
- Post — transfer each debit and credit to its account in the ledger.
- Trial balance — list every account's balance and confirm the columns agree.
- Report — roll the balances up into the income statement and balance sheet.
Three things to carry forward:
- The equation is an identity. Assets = Liabilities + Owner's Equity holds after every transaction, without exception.
- Every entry has two equal sides. Debits equal credits, so recording a transaction can never, by itself, unbalance the books.
- A trial balance proves equality, not truth. Ties are necessary but not sufficient — a wrong account can still balance.
Posted account by account, these balanced entries roll up into the trial balance, and from there into the income statement and balance sheet. Next: §2.2 Analyzing and Recording Transactions.