Credit Creation by Commercial Banks: Deposits and Multiplier

A question gives you an initial deposit of Rs 25,000 and a reserve ratio of 20%. You divide 25,000 by 0.20 and get Rs 1,25,000. Then the answer says newly created credit is Rs 1,00,000.

Where did the missing Rs 25,000 go?

Nowhere. The two figures answer different questions. Rs 1,25,000 is total deposits, including the initial deposit. Rs 1,00,000 is the additional lending and derivative deposits in this simplified example.

Once you can tell those amounts apart, credit creation becomes much easier. Let’s follow the money, build a complete table, and then solve the questions that tend to cause trouble.

What is credit creation by commercial banks?

Credit creation is the process through which commercial bank lending creates deposit money. When a bank grants a loan by crediting the borrower’s account, the borrower receives a spendable bank balance and also owes the bank a debt.

The bank records a loan asset and a deposit liability. It has created a deposit, but it has not given the borrower free wealth.

The Bank of England’s explanation of money creation describes this loan-and-deposit relationship and explains why actual lending is constrained by profitability, regulation, and monetary policy.

For school numericals, we usually study a simpler model: a fresh cash deposit enters the banking system, banks retain a fixed reserve fraction, and lending generates successive deposits. Keep that model’s assumptions beside the formula.

If you want to revise where deposits fit into money supply first, read our Money and Banking guide.

Primary deposits and derivative deposits

A primary deposit, also called an initial or passive deposit in this context, is money deposited by a customer rather than a deposit created by a new bank loan. In the numerical below, it is fresh cash entering the banking system from the public.

A derivative deposit, also called a secondary or active deposit, arises from the bank’s lending activity. Loan proceeds may remain in the borrower’s account or pass to a seller’s account when the borrower spends them.

Point	Primary deposit	Derivative deposit
Origin in our example	Customer brings existing cash into a bank	Bank lending creates an additional deposit
Initial effect	Cash held by the public becomes a bank balance	A new deposit appears alongside a loan
Example	Meera deposits Rs 25,000 of cash	A bank grants a Rs 20,000 loan
Place in the final total	Included once	Added to the primary deposit

The word fresh matters. Moving Rs 25,000 from your account at Bank A to your account at Bank B changes where the deposit is held. It does not give the banking system an additional Rs 25,000 of deposits or reserves overall.

Similarly, depositing cash you already held does not, by itself, increase currency-plus-demand-deposits money supply: currency with the public falls and deposits rise by the same amount. The subsequent lending is the expansion we want to trace.

The reserve ratio and the assumptions behind the model

Let r be the fraction of deposits retained as reserves. A 20% reserve ratio means r = 0.20, so each bank retains one-fifth of the deposit received and lends the remaining four-fifths in the classroom sequence.

The standard calculation assumes:

1. The initial cash deposit adds reserves to the banking system.
2. Every bank uses the same fixed reserve ratio.
3. Banks lend the full amount available after required reserves, without keeping additional idle reserves.
4. Loan proceeds return fully as bank deposits, with no cash leakage to the public.
5. Willing, creditworthy borrowers are available throughout the process.
6. We ignore loan repayments, defaults, interest, fees, and other balance-sheet changes during the expansion.

These assumptions define the exercise. If the question changes one, reconsider whether the simple formula still applies.

The reserve percentage used throughout this article is hypothetical. It is not a statement of any current policy rate. Use the reserve ratio supplied in your question. Do not substitute a remembered rate or add other ratios unless the problem expressly tells you how to do so.

Credit creation process: a complete worked example

Meera deposits Rs 25,000 in cash at Bank A. The reserve ratio is 20%. Assume the banking system satisfies all the conditions above.

Round 1: Bank A

Bank A retains:

Rs 25,000 x 20% = Rs 5,000.

It lends the remaining:

Rs 25,000 - Rs 5,000 = Rs 20,000.

The borrower uses the loan to pay a supplier, who receives the payment at Bank B. After the payment settles, Bank A has Rs 5,000 in reserves and a Rs 20,000 loan asset supporting Meera’s Rs 25,000 deposit.

Meera’s deposit has not been reduced by the act of lending. The borrower’s loan deposit has moved to the supplier at Bank B.

Round 2: Bank B

Bank B receives the Rs 20,000 deposit and the corresponding settlement funds. It retains Rs 4,000 and lends Rs 16,000.

That loan is spent, and the recipient receives Rs 16,000 in Bank C.

Round 3 and later rounds

Bank C retains Rs 3,200 and lends Rs 12,800. The process continues, with each new deposit equal to 80% of the previous round’s deposit.

Round	Deposit received (Rs)	Reserve retained at 20% (Rs)	New loan (Rs)
1	25,000	5,000	20,000
2	20,000	4,000	16,000
3	16,000	3,200	12,800
4	12,800	2,560	10,240
5	10,240	2,048	8,192
All remaining rounds together	40,960	8,192	32,768
Limiting total	1,25,000	25,000	1,00,000

The remaining-rounds row is an aggregate, not one extra round. The limiting total includes the entire sequence, not just the first five banks.

Check the result in two ways:

• Required reserves: 20% of Rs 1,25,000 = Rs 25,000.
• Assets supporting deposits: Rs 25,000 reserves + Rs 1,00,000 loans = Rs 1,25,000.

The original cash has not multiplied into five stacks of banknotes. The banking system has a larger stock of deposit liabilities, matched by reserves and loans.

Why doesn’t the process continue without limit?

There can be indefinitely many smaller rounds in the mathematical model, but their sum is finite. Each round retains a fraction as reserves, leaving a smaller amount for the next loan.

Imagine marking half the remaining distance to a wall again and again. You can make many marks without making the room infinitely long. Here, the shrinking sequence has a definite total too.

Deposit multiplier formula: where 1/r comes from

Let:

• P = initial fresh cash deposit.
• D = total deposits supported after the full expansion.
• r = reserve ratio as a decimal.

At the limit, all the initial reserves are needed to support the deposits:

r x D = P

Therefore:

D = P / r

The simple deposit multiplier is:

k = 1 / r

The classroom multiplier treatment is covered in the NCERT Money and Banking chapter, section 3.3. Its fictional-bank balance sheet is a useful way to check that the deposit total and the loan total are different.

For our example:

k = 1 / 0.20 = 5

D = Rs 25,000 x 5 = Rs 1,25,000

If you prefer to see the rounds in the formula:

D = P + P(1 - r) + P(1 - r)^2 + …

This geometric series has sum P/r when 0 < r <= 1. You do not need to write the series in every answer, but it explains why adding only three or four rounds understates the final potential.

Total deposits versus net credit creation

For a fresh cash deposit P in this model:

Total deposits, D = P / r

Derivative deposits = D - P

Additional loans, L = P(1/r - 1)

Thus derivative deposits and additional loans have the same amount here. This equality belongs to the simplified model; it is not a claim that every real bank’s deposits always equal its loans.

If the question asks for…	Use…	With P = Rs 25,000 and r = 20%
Simple multiplier	1/r	5
First-round loan	P(1 - r)	Rs 20,000
Total deposits including the initial deposit	P/r	Rs 1,25,000
Derivative deposits or additional credit	P/r - P	Rs 1,00,000
Total reserves retained across all rounds	rD	Rs 25,000

Notice another useful link:

First-round loan x multiplier = total additional loans.

Here, Rs 20,000 x 5 = Rs 1,00,000. The initial reserve deduction has already happened in Rs 20,000, so subtracting Rs 25,000 again would be a mistake.

If an exercise uses “total credit creation” without defining it, show both totals: “Total deposits = Rs 1,25,000, of which derivative deposits/additional loans = Rs 1,00,000.” That makes your interpretation visible.

Six solved credit creation numericals

1. Find the multiplier, total deposits, and derivative deposits

Question: A fresh cash deposit is Rs 40,000 and the reserve ratio is 10%. Find the three amounts.

Solution:

r = 10/100 = 0.10.

k = 1/0.10 = 10.

D = Rs 40,000/0.10 = Rs 4,00,000.

Derivative deposits = Rs 4,00,000 - Rs 40,000 = Rs 3,60,000.

Check: 10% of Rs 4,00,000 is Rs 40,000, exactly the original reserve addition.

2. Find the initial deposit from total deposits

Question: Total deposits generated are Rs 6,40,000, including the initial deposit. The reserve ratio is 12.5%. Find the initial cash deposit and additional loans.

Solution:

r = 0.125 and k = 8.

P = D x r = Rs 6,40,000 x 0.125 = Rs 80,000.

L = D - P = Rs 6,40,000 - Rs 80,000 = Rs 5,60,000.

Here, dividing total deposits by r would multiply a figure that has already been expanded. Reverse the original relationship instead.

3. Find the initial deposit from derivative deposits

Question: Derivative deposits are Rs 2,40,000 and r = 25%. Find the initial deposit.

Solution:

k = 1/0.25 = 4.

Derivative deposits = P(k - 1).

Rs 2,40,000 = P x 3.

P = Rs 80,000.

Total deposits = Rs 80,000 + Rs 2,40,000 = Rs 3,20,000.

The tempting calculation Rs 2,40,000/4 gives Rs 60,000, but that treats derivative deposits as the total. Identify the given amount before choosing your equation.

4. Find the reserve ratio

Question: A fresh deposit of Rs 30,000 supports maximum total deposits of Rs 2,00,000. Find r as a percentage.

Solution:

r = P/D = 30,000/2,00,000 = 0.15.

Reserve ratio = 15%.

The multiplier is 1/0.15, approximately 6.67. A multiplier does not have to be a whole number.

Check: 15% of Rs 2,00,000 = Rs 30,000.

5. Compare two reserve ratios

Question: With a fresh deposit of Rs 60,000, compare potential expansion at reserve ratios of 10% and 20%.

Calculation	At 10%	At 20%
Multiplier	10	5
Total deposits	Rs 6,00,000	Rs 3,00,000
Additional loans	Rs 5,40,000	Rs 2,40,000

Potential total deposits fall by Rs 3,00,000. Potential additional loans also fall by Rs 3,00,000, because the initial deposit is unchanged.

Doubling the reserve ratio halves the multiplier in this model. It does not halve additional loans: Rs 2,40,000 is not half of Rs 5,40,000.

This compares two possible limiting outcomes. It does not predict that actual banks instantly cancel that amount of loans after a policy change.

6. Distinguish one bank from the whole banking system

Question: Bank A receives fresh cash of Rs 50,000. The reserve ratio is 20%, and the entire loan payment leaves Bank A for another bank. How much can Bank A lend in the first round, and what is the system’s total additional lending potential?

Solution:

Bank A’s first-round reserve = Rs 50,000 x 20% = Rs 10,000.

Its first-round loan = Rs 50,000 - Rs 10,000 = Rs 40,000.

System total deposits = Rs 50,000/0.20 = Rs 2,50,000.

System additional lending = Rs 2,50,000 - Rs 50,000 = Rs 2,00,000.

The Rs 2,00,000 belongs to the full banking-system sequence. It is not Bank A’s first-round loan when the proceeds leave that bank.

Why actual credit creation can be smaller

The simple multiplier is a conditional result. Several factors can prevent the assumed sequence from being completed.

Cash leakage: Some recipients keep loan proceeds as currency. That portion does not return as a deposit for the next round.

Excess reserves: Banks may retain more than the required minimum, reducing the amount passed into further lending.

Both qualifications are discussed in OpenStax’s explanation of bank money creation.

Insufficient suitable borrowers: Available lending capacity does not ensure that households and businesses want loans on the offered terms, or qualify for them.

Capital and liquidity constraints: A bank needs a cushion against losses and the ability to meet payments. A reserve-ratio calculation alone does not establish that a proposed loan is affordable or prudent.

Changes in interest rates, risk, and confidence: These affect both lending decisions and borrowing demand. Repayments can also offset the deposits created by new lending.

The Bank of England’s short money-creation guide is helpful here: it explains why loan creation, payments to other banks, repayment, and limits on lending must be considered together.

A small cash-leakage example

Return to the first Rs 20,000 loan in our main example. Suppose its recipient keeps Rs 5,000 as cash and deposits only Rs 15,000 at Bank B.

Bank B’s next loan is now:

Rs 15,000 x 80% = Rs 12,000.

Without that leakage, its loan would have been Rs 16,000. The next step is already Rs 4,000 smaller.

That is enough to explain the direction of the effect. Do not calculate a new whole-system total unless the question specifies what happens to cash and deposits in the subsequent rounds as well.

A small excess-reserve example

Suppose every bank is required to retain 20% but chooses to hold a further 5% of each deposit as reserves. The total retained fraction in this modified exercise is 25%.

With no cash leakage and all other assumptions unchanged:

D = Rs 25,000/0.25 = Rs 1,00,000.

Additional loans = Rs 1,00,000 - Rs 25,000 = Rs 75,000.

Be careful: the extra 5% here is expressly a percentage of deposits. “Five per cent of available funds” would describe a different calculation.

A reliable answer-writing sequence

For a process question, start with the meaning of credit creation. State the initial deposit and reserve ratio. Explain one round in words, show several rounds in a table, and calculate the limiting totals. Finish with the assumptions or limitations the question asks for.

For a numerical, use this order:

1. Name the given quantity and the required quantity.
2. Convert the percentage reserve ratio into a decimal.
3. Write the formula before substituting the amounts.
4. Label the result as total deposits, derivative deposits, or additional loans.
5. Check reserves against the initial cash deposit.

You can usually catch an error in less time than it takes to redo the whole solution. If your final deposit total multiplied by the stated reserve fraction does not equal the original fresh cash deposit in the standard model, revisit the formula or the arithmetic.

Common mistakes and how to correct them

Mistake	Correction
Using 1/20 for a 20% ratio	Use 1/0.20 = 5
Calling total deposits additional credit	Subtract the initial deposit when additional credit is requested
Multiplying an existing interbank transfer as fresh system cash	Check whether system reserves actually increased
Giving the full system result as one bank’s first loan	Separate the first-round loan from all-round lending
Adding only the displayed rounds	Use the multiplier for the limiting total
Treating a lower reserve ratio as a guarantee of more loans	State the assumptions and consider borrower demand and bank constraints
Assuming r = 0 means real banks can lend infinitely	Recognise that the simple formula is undefined there and other constraints still matter

Try these practice questions

Assume fresh cash enters the banking system, all loan proceeds are redeposited, and banks retain only the stated reserve fraction unless the question says otherwise.

1. P = Rs 18,000 and r = 10%. Find the multiplier, total deposits, and additional loans.
2. Total deposits are Rs 3,60,000 and r = 20%. Find the initial deposit.
3. Derivative deposits are Rs 1,80,000 and r = 25%. Find the initial deposit and total deposits.
4. P = Rs 45,000 and total deposits are Rs 3,00,000. Find the reserve ratio.
5. P = Rs 24,000 and r = 12.5%. Find the first-round loan and system additional loans.
6. P = Rs 10,000 and r = 100%. Find total deposits and additional loans.
7. A customer transfers Rs 70,000 from one existing bank account to another bank. Does the transfer itself add Rs 70,000 to banking-system deposits?
8. P = Rs 32,000. Every bank retains 20% required reserves plus an additional 5% of deposits. Find the limiting total deposits and additional loans.

Answers with quick working

1. k = 10; D = 18,000/0.10 = Rs 1,80,000; L = Rs 1,62,000.
2. P = 3,60,000 x 0.20 = Rs 72,000.
3. k = 4; P = 1,80,000/(4 - 1) = Rs 60,000; D = Rs 2,40,000.
4. r = 45,000/3,00,000 = 0.15 = 15%.
5. First-round loan = 24,000 x 0.875 = Rs 21,000; D = Rs 1,92,000; L = Rs 1,68,000.
6. k = 1; D = Rs 10,000; L = zero.
7. No. One bank loses the deposit and another gains it; the transfer itself does not expand the system total.
8. Retained fraction = 0.25; D = Rs 1,28,000; L = Rs 96,000.

Frequently asked questions

What is credit creation in simple words?

It is the creation of bank deposit money through lending. A bank loan credited to a customer’s account gives the customer a spendable deposit and a matching debt to repay.

What is the difference between primary and derivative deposits?

A primary deposit originates from a customer’s deposit of existing money. A derivative deposit results from bank lending. In a standard fresh-cash-deposit exercise, total deposits equal the primary deposit plus the derivative deposits.

What is the formula for the credit creation multiplier?

In the simple classroom model, the multiplier is 1/r, where r is the reserve fraction. For a 20% ratio, use 1/0.20 = 5. Multiply the initial fresh cash deposit by this multiplier to find total deposits, including the initial deposit.

Why do we subtract the initial deposit?

Subtract it when the question asks for derivative deposits or net additional credit. It was already present before the lending expansion. For example, total deposits of Rs 1,25,000 include the original Rs 25,000, leaving Rs 1,00,000 created through lending in our model.

Are derivative deposits and additional loans always equal?

They are equal in the simplified model used here, where the only assets are the fixed initial reserves and the newly created loans. Real bank balance sheets include other assets, liabilities, and transactions, so you should not turn that classroom equality into a universal rule.

Can an individual bank create credit?

Yes, a bank creates a deposit when it credits a new loan to an account. However, when the borrower pays someone at another bank, settlement funds leave the lending bank. Do not confuse one bank’s first-round lending with the full banking system’s expansion.

Does depositing cash immediately increase money supply?

If the measure includes currency with the public and demand deposits, depositing existing cash changes its composition: public currency falls and deposits rise equally. The later lending process can increase deposit money beyond that initial amount.

What happens when the reserve ratio increases?

With a fixed fresh cash deposit and the other model assumptions unchanged, the simple multiplier falls and maximum potential deposits decline. Actual credit also depends on demand for loans, bank decisions, and other constraints.

Why is credit creation limited?

The textbook model requires reserves and assumes full redepositing and lending. Cash leakage or additional reserve holding reduces its expansion. In practice, borrower quality, capital, liquidity, profitability, and monetary conditions also constrain lending.

What is the fastest way to check a credit creation answer?

In the standard model, multiply your total deposit figure by r. It should equal the initial fresh cash deposit. Then check that additional loans plus that initial deposit equal total deposits, and confirm that you have answered the quantity actually requested.