How does paying off debt to the bank work?

Question

So, I understand that banks create money by making loans which end up as deposits. But what I don't get, is how paying off debt works in the big picture. Let me explain.

Let's say Jim got a loan of \$100 from the bank. He now owes the bank \$100 + \$10 interest. Where is he getting the money to pay off the loan? All of the money in the economy is created by the bank. So in this simplified example does he get it from someone else who took out a loan? Multiple people? Let's say he sold apples to Sarah and Bob for \$60 each. He would be able to pay the \$110 he owes to the bank. But Sarah and Bob would have had to take out loans, so they would also be in debt to the bank. Where would they get the money to pay off their debt?

Does the economy depend on a majority of people being unable to pay their debt? But if that was the case, how would the bank make money? I must be missing something here.

Answer 1

The total nominal income of the domestic economy is equal to nominal GDP growth. This chart shows nominal GDP growth for the U.S.: link to FRED graph.

If you dig into the numbers, we see that nominal GDP growth is often higher than most interest rates. So total income is growing faster than interest costs.

You cannot look at one loan in isolation and hope to make sense of total flows of income. At any given time, new loans are continuously made, while old loans are paid down. Mortgages are typically the largest household sector debt in aggregate. New buyers get large mortgages, while existing homeowners slowly pay down debt. The net change is normally positive, which effectively finances construction. Construction in turn adds to GDP and hence incomes. This story is repeated in different forms across all types of debt.

Answer 2

Edited in response to down vote. To answer the question we need to describe a reasonable econometric model that shows what happens when the borrower repays principal and interest to the bank and we need an aggregate model for where these payments "come from" on the whole economy.

This four page paper shows the accounting context with a simplified model for hypothetical bank balance sheet and income statement:

https://www.richmondfed.org/~/media/richmondfedorg/publications/research/economic_brief/2012/pdf/eb_12-03.pdf

where one must recognize that income items listed in the income statement are broadly classified as revenue.

The following reference:

https://www.utm.edu/staff/bputman/put7.htm

Gives this accounting identity:

Assets + Expenses + Dividends = Liabilities + Owners' Equity + Revenue

Assets, Expenses, and Dividends are called debit balance accounts. These increase by a debit and decrease by a credit entry. If total debits have greater value than total credits then the account has a positive (debit) balance.

Liabilities, Equity, and Revenue are called credit balance accounts. These increase by a credit and decrease by a debit entry. If total credits have greater value than total debits then the account has a positive (credit) balance.

Temporary accounts are broadly classified as expenses, dividends, and revenue. When the books open at the beginning of an accounting period temporary accounts are set to zero. When the books close at the end of an accounting period the temporary accounts are reset to zero by an appropriate entry and the net result is a transfer to equity as retained earnings or net loss for the period.

For simplicity we classify bank assets as reserves, securities, and loans; we classify bank liabilities as deposits and other liabilities; and we want to see the sources and sinks of deposits on the balance sheet of a bank or banking sector. We will put the desired level, deposits, on the left side of the equal sign and put the sources and sinks on the right side as follows:

Deposits = Reserves + Securities + Loans + Expenses + Dividends - Other Liabilities - Equity - Revenue

Loans issued and repayment of loan principal for transactions with nonbanks:

$\Delta Deposits = \Delta Loans$

Securities purchased from nonbanks and securities sold to nonbanks:

$\Delta Deposits = \Delta Securities$

Bank expenses or dividend payments made to nonbank units increase deposits:

$\Delta Deposits = \Delta Expenses$

$\Delta Deposits = \Delta Dividends$

When nonbank units pay revenue to banks revenue increases and deposits decrease:

$\Delta Deposits = -\Delta Revenue$

where bank revenue includes items such as interest income, penalty fees, and fees for services. Negative interest rates have the same accounting pattern as fees.

Equity adjustment to close the books at the end of an accounting period:

$\Delta Equity = Revenue - Expenses - Dividends$

where the change in equity is positive, to register retained earnings, when revenue exceeds expenses and dividends for the period; and the change in equity is negative, to register a loss, when expenses and dividends exceed revenue.

Note the sources of Deposits are payments to non-bank customers shown as extending new Loans, purchasing securities, paying Expenses, and paying Dividends, which logically will increase the deposits of those who are paid by the bank or bank sector.

One sink of Deposits is repayment of loan principal by non-bank customers this would reduce Deposits on the left and Loans on the right side of the above identity and is consistent with an accounting based econometric model of how deposit levels are coupled to loan levels.

Another sink of Deposits is Revenue from interest payments or fees of non-bank customers which are recorded as a decrease of deposits and increase of Revenue. So the interest payments on loans decrease deposits, increase revenue, and tend to increase equity when revenue is closed to equity at the end of an accounting period.

Another sink of Deposits is a decrease of Deposits and increase of Other Liabilities. I call this "migration" because it happens exclusively on the liability side of the bank or aggregate bank sector balance sheet.

In an aggregate bank sector the payment of interest and principal has no external source since deposits must be generated and exist in the aggregate system before they can be reduced to repay principal of loans and to pay interest that tends to increase the revenue and equity of the bank or bank sector when it operates at a profit.

An individual bank can lose reserves and deposits due to withdrawal of currency or gain reserves and deposits in equal measure due to "deposit" of currency. However the banking sector as a whole tends to lose reserves and deposits due to the currency drain. The central bank would purchase securities from the non-bank sector to add reserves and deposits back to the aggregate bank sector to offset the currency drain. The central bank can provide reserve loans to banks which increase reserves and borrowing from the central bank under Other Liabilities.

The only central bank operation which increases deposits significantly is so-called large scale asset purchases (LSAP) also known as quantitative easing (QE) which add reserves and deposits in equal measure if the central bank purchases securities from nonbank sellers and this happens because the payments are cleared via the aggregate bank sector balance sheet. These transactions are designated non-borrowed reserves and occur for conventional monetary policy on a much smaller scale compared to LSAP/QE policy.

Note if a bank transacts directly with the central bank or another bank then reserves may change but deposits are not affected by these types of interbank transaction. If a nonbank transaction requires that deposit funds move from one bank to another then reserves must transfer or "tag along" with the movement of deposits. We are not showing these transactions for simplicity because the question is where nonbank customers get the funds to pay interest on aggregate loans. We are showing how banks create deposits via transactions with nonbanks since the nonbanks use these same deposits to repay principal and pay interest.