Loan Repayment and Deposit Destruction

Why Principal Repayment Changes Deposits

When a bank makes a loan and credits the borrower’s account at that same bank, it records a loan asset and a deposit liability. When the borrower later repays principal from that account, the bank records the reverse movement: the outstanding loan falls, and the deposit falls by the same amount. The deposit is not transferred to another customer in this simplified transaction; the bank’s deposit liability is reduced. This is why principal repayment is described as deposit destruction.

The phrase refers to a reduction in bank deposit money, not to cash being physically destroyed and not to a bank losing capital. The borrower’s deposit asset and debt liability both decline. On the bank’s balance sheet, its loan asset and deposit liability both decline. These statements assume a principal payment made from a deposit account held at the lending bank, with no fees or other transactions included.

Definition: A principal repayment is a payment that reduces the amount of loan principal still owed. If a borrower repays $P$ of principal from a deposit account at the lending bank, the borrower’s deposit asset and loan liability each decrease by $P$. The bank’s deposit liability and loan asset each decrease by $P$.

The Matching Balance-Sheet Entries

A bank balance sheet records assets on one side and liabilities plus capital on the other. For the transaction considered here, the relevant bank assets include loans, while the relevant liability is the customer deposit. Let $L$ denote the bank’s outstanding loan assets, $D$ its customer deposits, and $K$ its capital. A principal repayment $P$ changes these balances as follows:

L_{\text{after}}=L_{\text{before}}-P,\qquad D_{\text{after}}=D_{\text{before}}-P,\qquad K_{\text{after}}=K_{\text{before}}.

This is a book-entry transaction under the stated assumptions. The bank debits the borrower’s deposit account, reducing the deposit liability, and reduces the recorded loan asset by the principal received. The borrower records the same two decreases on the borrower’s own balance sheet: deposits are an asset and the debt is a liability.

\begin{aligned} \text{Borrower:}\quad &\Delta \text{deposit asset}=-P, &\Delta \text{loan liability}=-P,\\ \text{Bank:}\quad &\Delta \text{loan asset}=-P, &\Delta \text{deposit liability}=-P. \end{aligned}

The bank’s total assets decline by $P$, because its loan asset declines. Its total liabilities also decline by $P$, because its deposit liability declines. Capital does not change merely because principal is repaid. The transaction is neither revenue from principal nor an expense for the bank: it collects an amount already owed.

Key result: For a principal repayment made from a deposit at the lending bank, deposits and outstanding loans each fall by the principal amount. In this simplified transaction, reserves and bank capital do not change. The balance sheet remains balanced because an asset and a liability fall equally.

Worked Examples

Worked Example: A Single Principal Payment

A borrower has a deposit of $16,000 and owes $21,000 in principal to the bank holding that deposit. The bank’s starting balance sheet shows $30,000 of reserves, $90,000 of loans, $105,000 of deposits, and $15,000 of capital. The borrower repays $6,000 of principal from the account. Find the borrower’s new balances and the bank’s balance sheet after the payment.

Method. Apply the same principal amount to the borrower’s deposit and loan balances, then record the matching changes in the bank’s deposit liability and loan asset.

The borrower’s deposit becomes $ \$16{,}000-\$6{,}000=\$10{,}000 $. The borrower’s principal outstanding becomes $ \$21{,}000-\$6{,}000=\$15{,}000 $.

The bank’s loans become $ \$90{,}000-\$6{,}000=\$84{,}000 $. Its deposits become $ \$105{,}000-\$6{,}000=\$99{,}000 $. Reserves remain $30,000, and capital remains $15,000 under the stated assumptions.

Before payment, the bank’s assets total $ \$30{,}000+\$90{,}000=\$120{,}000 $; deposits plus capital total $ \$105{,}000+\$15{,}000=\$120{,}000 $. After payment, assets total $ \$30{,}000+\$84{,}000=\$114{,}000 $; deposits plus capital total $ \$99{,}000+\$15{,}000=\$114{,}000 $. The balance sheet balances before and after. Common mistake avoided: treating the $6,000 principal collection as income that increases capital. Principal collection reduces the loan asset; it is not interest revenue.

Worked Example: Two Repayments and the Cumulative Change

A customer starts with $12,000 in a deposit account at the lending bank and owes $10,000 in principal. The bank has $40,000 of reserves, $60,000 of loans, $88,000 of deposits, and $12,000 of capital. The customer first repays $4,000 of principal and later repays another $2,500, both from the same account. Calculate the customer’s ending balances and the bank’s ending balances.

Method. Add the principal payments to find the total loan reduction, and check that the deposit account has enough funds for both payments.

Total principal repaid is $ \$4{,}000+\$2{,}500=\$6{,}500 $. The account can fund the payments: after the first payment it has $ \$12{,}000-\$4{,}000=\$8{,}000 $, which is enough for the second payment. After the second payment, the deposit is $ \$8{,}000-\$2{,}500=\$5{,}500 $. The remaining loan principal is $ \$10{,}000-\$6{,}500=\$3{,}500 $.

For the bank, loans end at $ \$60{,}000-\$6{,}500=\$53{,}500 $, and deposits end at $ \$88{,}000-\$6{,}500=\$81{,}500 $. Reserves remain $40,000 and capital remains $12,000. The ending assets total $ \$40{,}000+\$53{,}500=\$93{,}500 $. The ending liabilities and capital total $ \$81{,}500+\$12{,}000=\$93{,}500 $, so the balance sheet balances.

The deposit reduction is $6,500 in total, not $4,000 or $2,500 alone, because both payments reduce the account. Common mistake avoided: calculating each payment separately but failing to carry the first payment’s effect into the ending balances.

Worked Example: Separating Principal from Interest

A borrower has $24,000 of principal outstanding and a deposit of $9,000 at the lending bank. The bank’s opening balance sheet has $18,000 of reserves, $52,000 of loans, $60,000 of deposits, and $10,000 of capital. The borrower makes a $5,300 installment from the deposit: $5,000 is principal and $300 is interest income for the bank. Find the borrower’s ending deposit and debt, and the bank’s ending loans, deposits, and capital. Assume the interest is retained by the bank, with no expenses or distributions.

Method. Split the installment into its principal and interest components. The whole installment leaves the borrower’s deposit, but only the principal component reduces the loan asset.

The borrower’s ending deposit is $ \$9{,}000-\$5{,}300=\$3{,}700 $. The borrower’s remaining principal is $ \$24{,}000-\$5{,}000=\$19{,}000 $.

The bank’s loan assets fall only by principal: $ \$52{,}000-\$5{,}000=\$47{,}000 $. Its deposits fall by the full payment: $ \$60{,}000-\$5{,}300=\$54{,}700 $. The $300 interest income increases retained capital from $10,000 to $10,300. Reserves remain $18,000.

Check the balance sheet. Assets total $ \$18{,}000+\$47{,}000=\$65{,}000 $. Deposits plus capital total $ \$54{,}700+\$10{,}300=\$65{,}000 $. The entries balance. Common mistake avoided: reducing the loan by the whole $5,300. That would overstate the principal reduction by $300; the interest component is income, not principal repayment.

Why the Balance Sheet Stays Balanced

The accounting result follows directly from the balance-sheet identity. Before repayment, write the bank’s balance sheet as assets equal liabilities plus capital. For the transaction here, the bank’s assets include loans, and its liabilities include deposits. If the principal payment is $P$, loans and deposits each fall by $P$, while capital is unchanged.

\begin{aligned} \text{Before:}\quad A &= D+K,\\ \text{After:}\quad A-P &= (D-P)+K. \end{aligned}

The second line follows by subtracting $P$ from both sides of the first. Thus, if the bank’s balance sheet balanced before the payment, it still balances afterward. This explains the matching amounts: reducing the loan without reducing a liability or changing another balance-sheet item would leave the accounting identity unsatisfied. In the stipulated deposit-funded repayment, the deposit liability is the matching reduction.

The corresponding money interpretation is conditional on the payment source. A deposit held at the lending bank is reduced, so bank deposits fall by the principal amount. If the borrower pays from a different source or a different bank, additional entries may be needed; the simple same-bank entry described here is not a complete account of those arrangements.

Common Mistakes and Exam Traps

The most important check is to identify exactly what part of a payment is principal and where the payment comes from. Apply the principal amount to the loan balance, and apply the amount actually debited to the deposit account to deposits.

Reducing only the loan. If principal is paid from a deposit at the lending bank, the deposit liability also falls. Leaving deposits unchanged misses the matching entry.
Calling principal repayment bank income. The bank receives repayment of an asset it already recorded. Principal alone does not increase capital.
Reducing the loan by an entire installment. An installment may include interest. The loan falls by the principal component, while the deposit falls by the full amount charged.
Assuming reserves must fall in this book-entry example. The borrower’s account and loan are both at the same bank, so the stated transaction requires no reserve movement. Do not add a reserve change without a transaction that calls for one.
Interpreting “deposit destruction” literally. The term describes a decrease in recorded deposit liabilities. It does not mean cash is physically destroyed or that the bank incurs a capital loss.

A reliable check is to write the before-and-after amounts for loans, deposits, and capital, then verify that assets equal liabilities plus capital. If the account is debited by a combined installment, also check that the loan reduction uses principal alone.

Key takeaway: In a same-bank, deposit-funded principal repayment, the borrower’s deposit and debt fall by the principal amount, and the bank’s deposit liability and loan asset fall by that same amount. Principal repayment contracts deposits; by itself, it does not change bank capital.

Check Your Understanding

For each problem, assume the payment is made from a deposit account at the lending bank unless stated otherwise. Check both the borrower’s balances and the bank’s balance sheet where requested.

A customer has $7,500 on deposit and owes $9,000 of principal. The customer repays $2,000 of principal. What are the new deposit and principal balances? (Answer: Deposit $5,500; principal $7,000.)
A bank has $22,000 of reserves, $68,000 of loans, $79,000 of deposits, and $11,000 of capital. A borrower repays $8,000 of principal from an account at that bank. Give the ending loans and deposits, and verify that the balance sheet balances. (Answer: Loans $60,000; deposits $71,000; assets and liabilities plus capital each total $82,000.)
A borrower begins with a $15,000 deposit and $13,000 of principal outstanding, then makes principal payments of $3,500 and $4,000 from that account. Find the ending deposit and principal, and state the cumulative deposit reduction. (Answer: Deposit $7,500; principal $5,500; cumulative deposit reduction $7,500.)
A borrower pays $2,750 from a deposit account: $2,500 is principal and $250 is interest retained by the bank. The bank begins with $14,000 of loans, $20,000 of deposits, and $6,000 of capital. Find the ending balances for these three items. (Answer: Loans $11,500; deposits $17,250; capital $6,250.)
A borrower’s deposit at the lending bank is $4,000, and the borrower owes $6,000 in principal. The borrower makes a $5,000 principal payment from that account. Is the payment fully fundable from the stated deposit, and what balance-sheet conclusion can be drawn without adding another funding source? (Answer: No; the account is short by $1,000, so the stated same-account transaction cannot be completed as described. Do not record a $5,000 deposit reduction without specifying an additional source.)

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