Bank A
| Assets | Liabilities + equity | ||
|---|---|---|---|
| reserves | 100 | deposits | 300 |
| loans | 200 | borrowing | 0 |
| bonds | 40 | equity | 40 |
| Total | 340 | Total | 340 |
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Monetary systems · Lesson 5
Repayment, interest, and loan losses
Distinguish deposit destruction from a bank absorbing a loss.
By the end: Trace principal repayment, interest income, and write-downs without treating them as the same operation.
Principal repayment reverses origination
A borrower uses 40 from a deposit at the lending bank to repay principal. The bank reduces its loan asset by 40 and its deposit liability by 40. The borrower loses a deposit asset and reduces a debt by 40. Under these assumptions, deposit money is extinguished. The bank does not receive a new asset called repaid principal in addition to the remaining loan.
If payment comes from a different bank, settlement moves reserves first. Across the banking system, the borrower's deposit and the lending bank's loan asset still decline. The receiving bank gains reserves as its loan asset falls, while the sending bank loses reserves and its deposit liability. A bank can use the resulting liquidity, but cannot re-lend an accounting entry called the original deposit.
Separate the amount owed from the payment instrument
A loan principal is the outstanding amount borrowed, before distinguishing interest and fees. Repaying principal reduces that outstanding claim. A deposit is a payment asset held by the customer and an obligation of the bank. When both claims belong on the same bank's books, principal repayment can cancel part of the loan asset against part of the deposit liability. It is not necessary for the bank to receive physical currency or a reserve transfer. The bank owes the customer less, and the customer owes the bank less, by the same agreed amount.
Consider an additional paper case using the opening bank balances. A has reserves 100, loans 200, bonds 40, deposits 300, and equity 40. One customer has a deposit of 70 and owes principal of 90 included within those totals. The customer repays 25 of principal from that account. Their deposit becomes 45 and debt becomes 65. A's aggregate loans become 175 and deposits become 275. Assets are now 315, while deposits of 275 plus equity of 40 also total 315. No new reserve asset appears, and the bank has not earned income of 25.
The customer's financial net worth is unchanged by this principal-only payment. Before payment, a deposit of 70 less debt of 90 gives negative 20. Afterward, a deposit of 45 less debt of 65 still gives negative 20. The customer has less immediately spendable money and less debt. Their exposure to future contractual interest may also change, depending on the contract, but that is separate from these initial balances. Paying a debt is therefore not automatically an expense equal to the payment. Principal repayment exchanges a reduction in one asset for a reduction in one liability.
Now put the customer's deposit at B while the loan stays at A. B reduces its customer deposit liability by 25 and sends A 25 in reserves. A increases reserves by 25 and reduces its loan asset by 25. A exchanges one asset for another; B's assets and liabilities both shrink. Across the two banks, reserves are unchanged, deposits fall by 25, and loan assets fall by 25. This is the same system-wide contraction in deposits as repayment within A, but the distribution of bank liquidity differs. The receiving lender now holds more settlement assets.
These entries assume the customer has enough deposits and the payment is applied to principal. A scheduled installment may include principal, interest, and fees, each requiring its own treatment. An overdue amount may remain legally payable even if no payment arrives. A bank can also refinance a loan by issuing new credit that repays old principal. In that case, repayment of one claim and creation of another must both be recorded. Observing an old loan disappear does not by itself show a reduction in the banking system's total lending or deposits.
Interest is income, not principal
Interest compensates the lender under the contract and is distinct from repayment of principal. If a customer pays 4 interest from a deposit at the lending bank, its deposit liability falls by 4 and bank income rises by 4. With no expenses or taxes in this entry, equity rises by 4. The loan principal is unchanged. Real accounting may accrue interest before payment; here income is recognized on payment for simplicity.
A bank then pays wages, suppliers, taxes, or dividends. These transactions have their own counterparts and can put deposits back into nonbank hands. Therefore it is wrong to infer that the original principal must include all future interest money, or that interest payments mechanically require an ever-expanding debt stock. The same money can circulate through multiple incomes and payments. Distribution, defaults, and contractual affordability still matter.
Trace income through interest and spending
Use an additional payment example to distinguish income from principal. A customer pays 32 from a deposit at A, with 28 assigned to principal and 4 to interest. Begin with A's opening assets of 340 and deposits of 300. Principal falls by 28, so loan assets become 172 and total assets become 312. Deposits fall by all 32 to 268. With income recognized on payment and no other costs, equity rises by 4 to 44. Add 268 and 44 to obtain 312. Assigning the whole payment to principal would misstate both remaining debt and bank income.
The customer gives up an asset of 32 but reduces a liability by only 28. Their net worth falls by 4 through the interest expense. A's equity rises by 4 through interest income before expenses. These are the two sides of the income transfer. The bank does not need to put that 4 into a separate cash container for equity to increase. Its deposit liability has fallen without an equal fall in assets. The residual belonging to shareholders therefore rises. A bank balance sheet can change through an income entry even when its reserves do not move.
Real accounts often recognize interest as it is earned rather than waiting until payment. That process is called accrual. Suppose A has already recognized 4 of interest receivable, a claim to interest not yet collected, and the associated income. Collection then replaces or removes that receivable rather than recording another 4 of fresh income. The customer's payment still reduces their deposit, but the bank must not count the same earnings twice. The simplified payment-time example deliberately omits this earlier recognition so the difference between principal and income remains visible.
A bank's spending can return deposits to customers. Suppose, in a separate paper case, A receives interest of 6 from a customer account, then pays a worker 4 into an account at A. The first entry reduces deposits by 6 and raises equity by 6. The wage payment increases the worker's deposit by 4 and reduces equity by 4 as an expense. Across those two entries, deposits fall by 2 and equity rises by 2. If the worker banks elsewhere, A also needs a settlement transfer. The income and expense still have different counterparts from principal repayment.
A money stock is measured at a date, whereas interest income is a flow over a period. A deposit balance of 10 can pay interest of 2, then pass to a worker through bank spending, then pay for goods, and later finance another payment. Adding all payments over a year can exceed the deposit stock observed at one moment. This arithmetic refutes a claim that all future interest must exist as extra deposits on the day a loan originates. It does not prove every borrower can earn enough income on time. Contract dates and the distribution of receipts remain constraints.
Work through the accounts and assumptions
Inspect both banks' books
Currency units. Both banks remain visible. Δ means change from the opening snapshot. Choose a named experiment; changing it resets playback and all balances.
Opening balance sheets
Bank B
| Assets | Liabilities + equity | ||
|---|---|---|---|
| reserves | 100 | deposits | 300 |
| loans | 200 | borrowing | 0 |
| bonds | 40 | equity | 40 |
| Total | 340 | Total | 340 |
System deposits: 600. System reserves: 200.
Each bank has 340 assets, 300 deposit liabilities, and 40 equity. No cash or other banks are included.
Step 0 / 1
All stages and totals
| Stage | Deposits | Reserves | A equity |
|---|---|---|---|
| Opening balance sheets | 600 | 200 | 40 |
| A customer repays 60 principal | 540 | 200 | 40 |
Opening balance sheets. Each bank has 340 assets, 300 deposit liabilities, and 40 equity. No cash or other banks are included.
A customer repays 60 principal. Assume the borrower already has enough deposits at A. Both the loan asset and deposit liability fall; reserves and equity do not change.
| Event at lending bank | Loan asset | Deposit liability | Equity |
|---|---|---|---|
| Principal repaid 40 | −40 | −40 | Unchanged |
| Interest paid 4 | Unchanged | −4 | +4 before costs |
| New loan loss 30 | −30 | Unchanged | −30 |
Compare a paid loan with an impaired loan
The Principal repayment experiment begins again with each bank holding reserves 100, loans 200, and bonds 40, matched by deposits 300 and equity 40. A customer repays 60 using sufficient deposits already at A. A's loans fall to 140 and deposits to 240. Its assets total 280, matched by deposits 240 plus equity 40. B remains at its opening balances. System deposits decline from 600 to 540, while system reserves stay 200. The experiment supplies the customer's deposits as an assumption; it does not show how the customer earned them.
Select Loan loss to compare a different transaction from the same opening snapshot. A again ends with loans of 140 and total assets of 280. This time deposits remain 300. For the books to balance, equity falls from 40 to negative 20. System deposits remain 600. Matching final loan totals therefore do not imply matching economic events. Repayment removed both a loan asset and a deposit liability. The loss removed loan value without removing the bank's obligations to depositors. The displayed negative equity records the shortfall rather than fixing it.
The named scenarios are separate experiments, not commands that accumulate on one shared bank. Choosing Loan loss after Principal repayment does not apply a second 60 reduction to loans already reduced to 140. Both scenarios restart from loans 200. Reset returns the selected scenario to its opening stage. The visible change labels also compare with that opening stage. This allows a controlled comparison of two outcomes under the same initial conditions. There is no interest-payment scenario or control for combining principal and interest in this widget; those cases belong to the paper calculations.
For another paper comparison, suppose A previously lent 45 and the borrower paid it to a supplier at B. At origination A added loans 45 and deposits 45. Settlement then moved reserves 45 to B and moved the deposit claim to the supplier's bank. Later A discovers that 15 of the loan's value cannot be recovered. A reduces its loan asset and equity by 15. B has no corresponding reason to reduce the supplier's deposit. The supplier was paid for a sale; the supplier did not promise to cover the borrower's future failure.
There can be separate legal reasons to reverse a payment or impose losses on creditors, but neither follows automatically from recognizing a loan impairment. The model contains no court order, insurance payout, creditor conversion, or bank resolution procedure. It also does not record individual borrower liabilities. Read its loss as a change in the bank's assessed loan value under the stated absence of prior allowance. Do not infer that the customer's legal debt fell by exactly the same amount, or that a different customer's deposit was secretly canceled to make the bank whole.
A loss is not a repayment
If a bank recognizes that 30 of a loan asset will not be recovered, the asset falls by 30. A previously unrecognized loss reduces equity by 30, leaving customer deposits unchanged. The deposit created when the loan originated may have long since moved to someone else. It does not automatically disappear because the borrower defaults.
Loss provisions may recognize expected losses earlier, so a later write-off against an existing allowance need not cause another equity hit. A bank's accounting write-off also need not legally forgive the borrower's debt. Our loss scenario shows one fresh asset impairment with no prior allowance. It is neither a full insolvency proceeding nor a claim that all defaulted debts are canceled.
Recognizing a loss and writing off a claim
Expected-loss accounting can separate recognition of damage from removal of a gross loan balance. Consider an additional paper example with gross loans of 100 and no initial allowance. The bank estimates that it will recover only 88. It records an allowance of 12 against the loan asset and an expense of 12, reducing equity by 12. Net loan value is 88 because the allowance reduces the reported value of the gross claim. Deposits do not change. The bank has recognized an expected shortfall without recording a principal payment or necessarily changing what the borrower legally owes.
Suppose the bank later writes off 12 using that existing allowance. Gross loans fall from 100 to 88 and the allowance falls from 12 to zero. Net loan value stays 88. Charging another 12 to equity would count the same loss twice. If the bank instead discovers an additional shortfall of 5 not covered by the allowance, that new information requires another loss of 5 under these assumptions. Timing matters because a headline about a write-off may describe removal of an already provided amount rather than a fresh hit to current income.
A recovery has its own entries too. If a bank receives 3 on a claim previously written off completely, and there is no remaining recorded asset for that portion, collection can create recovery income. Payment from the customer's account at the same bank reduces deposits by 3 and increases equity by 3 under this simplified treatment. Payment from another bank brings reserves instead. Recovery income is not evidence that the original loss destroyed the supplier's money and then recreated it. The bank's asset valuation and the location of the payer's deposit answer different accounting questions.
Bank accounting and borrower obligations need separate records. A lender may conclude that collection is unlikely while still retaining a legal claim. A formal agreement forgiving debt may reduce the borrower's obligation, but the treatment depends on the agreement and applicable law. If a borrower owed 50 and a legally effective settlement requires only 35, the borrower can record a reduction in obligations according to those terms. That is not the same event as a bank privately marking a loan down to its expected recovery value. Our widget does not decide enforceability, tax treatment, or forgiveness.
Use these distinctions when comparing changes in published loan stocks. A portfolio can shrink through principal payments, sales to another holder, write-offs, or changes in valuation. A sale at recorded value exchanges a loan asset for another asset; it need not extinguish the borrower's debt. A write-off can remove a recorded claim without a payment. New lending can offset repayments during the same period. To explain a change in deposits, trace deposit entries and counterparties rather than assuming that every reduction in the loan stock destroys the same amount of money. That conclusion is valid for the specified repayment mechanism, not for all reductions in reported loans.
Exercises
Split a payment
A borrower pays 55 from its deposit at the lending bank: 50 principal and 5 interest. Ignore prior accruals, costs, and taxes. What changes?
Hint
Treat it as two entries.
Worked answer
| Entry | Loan asset | Deposit liability | Equity |
|---|---|---|---|
| Principal | −50 | −50 | 0 |
| Interest | 0 | −5 | +5 |
| Combined | −50 | −55 | +5 |
The loan asset falls by 50, the deposit liability by 55, and equity rises by 5. Assets fall 50, and liabilities plus equity also fall 50. Counting all 55 as principal would understate the remaining debt.
The money survives a default
A bank previously lent 70, which the borrower paid to a seller. The bank now recognizes an unprovided loss of 20. Does the seller's deposit fall?
Hint
The seller is not making a payment or agreeing to a debt reduction.
Worked answer
| Affected claim | Change |
|---|---|
| Lender loan value | −20 |
| Lender equity | −20 |
| Seller deposit | 0 |
No. The lending bank loses 20 of loan value and 20 of equity. The seller's deposit remains a claim on its own bank. Only a separate transaction or resolution measure could change that claim.
Sources and further reading
These references support the mechanisms and identify institutional context. They are optional; the explanations and worked answers above stand alone. Numerical examples are teaching cases, not live financial data or personal financial advice.
- Bank of England: Money creation in the modern economy, 2014
Bank lending, deposit creation and destruction, constraints, and asset purchases. UK institutional explanation, not a universal timetable or a current rate announcement.
- Bank of England: What is capital?
Loss absorption and prudential oversight. Our equity-to-assets example is deliberately simpler than regulatory capital rules.