Keep deposits, reserves and loans distinct

Keep deposits, reserves and loans distinct

Start with a payment, not a multiplier

A shop receives a customer’s bank transfer. The customer sees one deposit fall and the shop sees another rise. What moves between the banks? What if the customer originally obtained money through a loan? Use the two-bank ledger to follow the separate claims instead of imagining that every entry is the same pile of cash.

All figures here are invented credits. The original fixed source packet describes one loan and one transfer. The laboratory extends it with a receiving bank, a principal repayment, a rejected-payment case and an asset loss. Keep the original example separate from the settings you change.

Read a balance sheet from the bank’s perspective

A loan is the bank’s asset because the borrower owes the bank. The borrower’s deposit is the bank’s liability because the bank owes the account holder. A reserve balance is a settlement asset the bank can transfer to another bank in this model. These are different relationships, even when they use the same unit.

Equity is the residual difference between assets and liabilities. It is not a cash box or a reserve balance. For A, reserves 20 plus loans 80 make assets 100; deposit liabilities are 90, leaving equity 10. B also has assets 100, deposits 90 and equity 10, but holds reserves 30 and loans 70. Similar totals can conceal different liquidity positions.

Read the identity assets = liabilities + equity aloud: what the bank holds equals what it owes plus the owners’ residual claim. If recorded assets fall below liabilities, equity becomes negative and the identity still holds. An equation balancing is an accounting check, not a safety certificate.

Inspect five steps manually

Select each numbered ledger step. There is no timed animation: the bank cards, explanation and complete ledger table describe the same calculation. On a narrow screen, use the cards and step selector instead of scrolling across the whole table.

1. Opening: A has reserves 20, loans 80, deposits 90 and equity 10; B has reserves 30, loans 70, deposits 90 and equity 10.
2. Loan: A credits a new loan of 10 and creates a deposit of 10. Its loans become 90 and deposits 100. Reserves and equity stay unchanged.
3. Principal repayment: At the default repayment of zero, nothing changes. If the new borrower repays 4 from that deposit at A, loans and deposits both fall by 4. There is no reserve transfer for this internal repayment.
4. Payment: A different existing depositor pays 15 to someone at B. A’s reserves and deposits each fall by 15; B’s reserves and deposits each rise by 15. This is settlement between banks, not repayment of the new loan.
5. Loan loss: At the default loss of zero, nothing changes. A selected loss reduces the recorded value of A’s old loans and its equity together. No customer payment occurs, and deposits are not canceled.

Every change recomputes these steps from the original balances. Moving a slider twice does not make two cumulative payments. The final receipts report accepted amounts even when the selected ledger step is earlier in the sequence.

Reproduce the original worked example

Reset the experiment: loan 10, repayment 0, transfer 15, loss 0. A ends with reserves 5, loans 90, deposits 85 and equity 10: 5 + 90 = 85 + 10 = 95. B ends with reserves 45, loans 70, deposits 105 and equity 10: 45 + 70 = 105 + 10 = 115.

Across both banks, deposits rise from 180 to 190 because of the loan. The transfer changes where deposits are held, not their combined total. Reserves remain 50 across the two banks. Do not add those 50 to customer deposits and call the sum the same kind of money; reserves are an interbank claim in this model.

Change one thing: principal repayment

Keep loan 10 and transfer 15, but set repayment to 4. Before the transfer, A has loans 86 and deposits 96. Afterward, A has reserves 5, loans 86, deposits 81 and equity 10. B still has deposits 105, so system deposits are 81 + 105 = 186. The net increase is loan 10 minus actual repayment 4, or 6.

Why not call the repayment bank income? Principal reduces the loan claim and the deposit used to pay it. Interest and fees would require different entries; neither is included here. Nor is a loss the same event as repayment: a write-down does not receive a customer’s deposit payment.

The repayment control applies only to this newly created loan, using its still-unspent deposit. A request greater than the new loan is rejected entirely, not silently capped. Try loan 5 with requested repayment 6: actual repayment is zero. This is a precise teaching contract, not a general claim that borrowers cannot use other funds or repay older debt.

Separate a liquidity shortfall from an asset loss

Return repayment and loss to zero. Compare transfer 20 with 21. The first uses all A’s opening reserves. The second cannot settle under the model’s rules, so neither bank moves a reserve or deposit entry. A still has positive equity; it lacks the specified settlement asset for that payment at that moment.

A real bank may seek funding, sell assets or access other facilities. This exercise omits those actions so that settlement is visible. It does not claim that current reserves mechanically determine how much a bank can lend, or that any balance-sheet expansion is acceptable.

Now set transfer to zero and loss to 11. A still has 20 reserves, but its equity falls from 10 to −1. Its recorded assets are below deposit liabilities. With loss exactly 10, equity is zero: no buffer remains, which is different from negative equity and still not a guarantee of safety. Keep payment capacity and book net worth in separate sentences.

Reconcile the system

For this scenario, let L be the new loan, R the actual accepted principal repayment, T the accepted transfer and W the write-down. Each is in credits. They are amounts within this one sequence, not rates per year.

• A’s final reserves are 20 − T; B’s are 30 + T. Their sum remains 50.
• A’s final loans are 80 + L − R − W. B’s loans remain 70.
• A’s final deposits are 90 + L − R − T; B’s are 90 + T. Their sum is 180 + L − R.
• A’s equity is 10 − W; B’s remains 10.

The transfer cancels out when adding across banks. The loss changes assets and equity, while lending and principal repayment change both loan assets and customer deposits. These equations record the stated accounting transactions. They do not predict credit demand, spending, output or inflation.

Repair a plausible claim

Claim needing revision: “A new loan uses up reserves, and writing it off deletes the borrower’s deposit, so all four controls shrink system money.”

Before checking the explanation, identify which two entries move in each step and write a repair in your saved claim. Use two captures with different settings as evidence.

Compare your repair with a supported explanation

In this ledger, lending raises a loan asset and a deposit liability without immediately changing reserves. Principal repayment from that deposit reduces both entries. Settlement transfers reserves and reallocates deposits between banks without changing either system total. A write-down reduces the old loan asset and equity, leaving deposits unchanged. The initial claim confuses different transactions and treats reserves as customer deposits. A stronger completed answer cites captured settings and explains the model’s funding and valuation limits.

Try an unfamiliar ledger

Work this case on paper or in your saved claim before opening the check. A different fictional bank C starts with reserves 12, loans 48, deposits 54 and equity 6. It creates a new loan and deposit of 8. The new borrower repays principal 3 from that deposit. An existing depositor then requests an outward payment of 13, under the same no-borrowing/no-asset-sale rule. Finally the bank recognizes a loss of 7 on old loans.

State the final four balances. Explain whether the payment settles, whether equity is positive, and why neither answer follows merely from the ledger balancing. This is additional guided practice, not a separately certified independent assessment.

Check the unfamiliar ledger after attempting it

The payment of 13 exceeds reserves of 12 and is rejected in full. Final reserves are 12, loans 48 + 8 − 3 − 7 = 46, deposits 54 + 8 − 3 = 59, and equity 6 − 7 = −1. Assets 58 equal liabilities 59 plus equity −1. The payment shortfall and negative book equity are separate findings. If the payment request had been 12 instead, reserves and deposits would each fall by 12; that would not undo the asset loss.

Extend the investigation with evidence

For high-school work, annotate the paired entries and explain one rejected request. For AP practice, use a balance-sheet argument to distinguish deposit creation, settlement and principal repayment; compare this model’s assumptions with the current course framework instead of treating it as a complete banking syllabus. For introductory college work, consult an authentic dated bank balance sheet or monetary-methods source, identify definitions and omitted funding or capital constraints, and explain which of the classroom entries it can illuminate. Do not infer a bank’s condition from one ratio or this fictional model.

Method reference: McLeay, Radia and Thomas, Money creation in the modern economy, Bank of England (2014). The article discusses deposit creation and constraints on lending; the numerical balances and rejected-request rules here are original teaching assumptions, not a reproduced institutional dataset.

Compare a textbook ceiling with finite lending rounds

The two-bank lab above follows specified transactions. The next workbench adds a different behavioral rule: banks lend the permitted remainder of each receipt, borrowers always accept, and all noncash spending is redeposited. The Bank of England reference explains why actual lending is not simply a mechanical multiplication of reserves. We use this conditional model to examine that distinction, not to replace the accounting lab.

Test a conditional expansion rule

Separate fictional textbook system, measured in credits. Initially a central-bank purchase from a nonbank creates 100 of bank reserves and a 100 customer deposit. We track only the resulting changes, with no initial public currency in this incremental ledger.

Required reserve fraction0%10%20% Extra fraction retained from each receipt0%10% Cash withdrawn from each new loan0%20% Completed lending rounds1412

For each incoming deposit receipt d, retain (required + extra) × d and lend the remainder. Borrowers hold the chosen fraction of each new loan as currency; the rest becomes the next bank's deposit receipt. Every available loan is demanded, approved and spent under this rule. No repayment, loss, new base injection or other constraint is modeled.

Receipt → retained reserves + new loan → public currency + next deposit receipt. Cash withdrawal reduces system bank reserves while increasing public currency by the same amount. The cash fraction is a share of each loan, not a currency-to-deposit ratio.

Solid line/points: completed rounds. Dashed line: conditional infinite-round limit, not a dated forecast. Round zero is the initial 100 deposit. A round is an accounting sequence, not a day.

After 4 rounds: deposits 409.51, public currency 0.00, bank reserves 100.00, new loans 309.51. Money total 409.51; money/base ratio 4.10.

Required reserves now: 40.95; reserves above that requirement: 59.05. This finite-round excess includes funds awaiting the next modeled lending step, as well as deliberate extra retention.

Base stays 100.00. Incremental bank assets: reserves 100.00 + loans 309.51 = deposits 409.51. Money created beyond the initial deposit: 309.51.

Each row describes one receipt and its use, rounded to two decimals

Round	Receipt	Retained	Loan	Cash	Next receipt
1	100.00	10.00	90.00	0.00	90.00
2	90.00	9.00	81.00	0.00	81.00
3	81.00	8.10	72.90	0.00	72.90
4	72.90	7.29	65.61	0.00	65.61

Next-receipt fraction q = (1 − required − extra) × (1 − cash fraction) = 0.90. Deposits include the last redeposit even though its next lending step has not yet occurred.

Conditional limits: deposits 1000.00, public currency 0.00, money 1000.00; money/base ratio 10.00.

The simple no-cash/no-extra-retention maximum is 1 / required fraction = 10.00. It is a conditional benchmark, not the observed finite ratio.

Restore reserve experiment

Controls are temporary. Save the settings and reasoning in the source notebook. This separate rule is not how the two-bank lab approves loans, nor a description of current monetary implementation.

Predict the first round

Set the required fraction to 10%, extra retention and cash withdrawal to zero, and complete one round. Before reading the output, calculate how much of the initial receipt is retained and lent. Then reconcile the whole banking system. Why are system reserves above the requirement even though the first receiving bank retained exactly its stipulated fraction?

Check the first reserve round

The first bank retains 10 and lends 90. The spent loan becomes a 90 deposit receipt elsewhere. System deposits are now 190; total loans 90 and reserves 100, so incremental assets 190 equal deposit liabilities 190. The system requirement is 10% of 190=19, leaving 81 above requirement. That includes the new recipient’s still-unlent funds. A single completed step has not exhausted the system’s conditional lending opportunities.

The base remains 100. Money/base is 190/100=1.9 after one round, while the no-leakage infinite-round benchmark is ten. Confusing the finite ratio with that benchmark would erase the time-independent sequence we are inspecting.

Derive the limit instead of memorizing a number

With no cash withdrawal or extra retention, each receipt is 90% of the preceding one. Deposits after one round are 100+90; after two, 100+90+81. The full geometric sum is 100/(1−0.9)=1,000. New loans total 900. Thus the model’s deposit increase from the initial 100 is 900, while its total deposit stock created by the injection is 1,000. The 100 initial injection is already included; do not add it twice.

More generally, the next-receipt fraction is q=(1−required−extra)×(1−cash fraction). If q is below one, total deposits approach 100/(1−q). Total loans approach 100×(1−required−extra)/(1−q), and currency equals the selected cash fraction times those loans. This explains why deposits alone and deposits plus currency have different multipliers when cash is withdrawn. These are limits of stipulated sequences, not measured forecasts.

Change a leakage and preserve the accounting

Keep the requirement at 10%. Compare two separate scenarios: extra retention 10% with no cash withdrawal; then extra retention zero with 20% of each loan withdrawn as cash. Inspect one, four and twelve rounds. Predict which entries shrink and whether the monetary base disappears. Show a deposit total and a deposits-plus-currency total before comparing limits.

Check retention and currency leakage

Extra retention gives q=0.8, deposits and money approaching 500, with loans approaching 400 and reserves staying 100. The 10% extra fraction is ten percentage points of each receipt, not 10% of the required fraction.

With 20% cash withdrawal and no extra retention, q=0.9×0.8=0.72. Limits are approximately deposits 357.14, loans 321.43, public currency 64.29 and bank reserves 35.71. Money is about 421.43, so money/base is about 4.21; the deposit/base ratio is about 3.57. The base remains 100 because 35.71 reserves plus 64.29 currency equals 100, subject to displayed rounding. Currency leakage changes where base money is held; it does not destroy base money in this experiment.

Test the boundary of the formula

Set both reserve fractions and cash withdrawal to zero. Compare one and twelve rounds. Then enable 20% cash withdrawal while keeping the reserve fractions zero. Explain why neither result establishes that actual banks can lend without constraint.

Check the zero-requirement boundary

Without any retention or cash withdrawal, every receipt is 100. One completed loan gives money 200; twelve give 1,300. The sequence has no finite infinite-round limit, and 1/0 is undefined. The interface does not label infinity as a usable forecast. With 20% cash withdrawal, q=0.8 instead, giving a conditional money limit of 600: deposits 500 plus currency 100.

Both results follow the invented behavioral rule. Capital, creditworthiness, profitability, funding, repayments, policy responses and actual demand can constrain real lending. A zero required-reserve ratio does not remove those constraints. Do not import this rule into the first lab, whose loan/settlement contracts are different.

Transfer: identify the initial transaction

A different fictional economy begins with the public holding 50 in currency. That currency is deposited into a bank; no central-bank asset purchase occurs. Under a 20% requirement, no extra retention and no later currency withdrawal, calculate the conditional final deposits, subsequent loans and change in money measured as deposits plus public currency. Compare the result with a new central-bank purchase of 50 from a nonbank when initial money in this incremental ledger is zero.

Check the initial-transaction comparison

Depositing existing currency initially exchanges public cash 50 for deposits 50; money remains 50. The conditional final deposits are 50/0.2=250, with 200 subsequent loans. Money increases by 200 from the original 50. The base remains 50, now held in the banking system under this simplified classification.

A new central-bank purchase in the separate zero-start ledger first creates a deposit and reserves of 50, then the same conditional lending sequence reaches 250. Relative to zero, the total money increase is 250; relative to the just-created initial deposit, subsequent expansion is 200. Same final amount, different initial transaction and comparison baseline. Neither result is a causal estimate for an actual asset-purchase program.

Retain the baseline transaction, settings, finite ledger and limit assumptions in your notebook. AP practice should distinguish required/excess reserves and money/base from the conditional maximum. College extension should compare the model’s causal story with the linked institutional explanation and a dated operating framework. Independent assessment needs unfamiliar balances and a justified boundary case without these open answers.