Short answer: Financial institutions pay you interest as a reward for letting them use your money, which they then lend or invest to earn a higher return. Details:

• Core idea: Banks and other lenders borrow money from depositors (you) and lend it out at higher interest rates. The difference between what they pay you and what they earn from borrowers is their profit, often called the net interest margin.
• Why pay interest: Depositors supply the funds that fund loans and investments. Paying interest keeps customers with that institution and provides a cheap funding source.
• How it works in practice:
  • Savings accounts and CDs: You earn a stated interest rate (APY) on your balance.
  • Loans and credit: Borrowers pay interest on mortgages, auto loans, credit cards, etc., which is higher than the rate paid to depositors.
  • The spread (the gap between what banks pay savers and what they earn from borrowers) funds operations, profits, and regulation-required reserves.
• Government and central-bank roles: In some cases, central banks pay interest on reserve balances held by banks (a separate mechanism) to influence liquidity and short-term rates. This is distinct from consumer savings account interest but follows the same basic principle of compensating banks for holding money.

Key terms to know:

• APY (Annual Percentage Yield): The actual yearly return on a deposit after compounding.
• Net interest margin: The difference between interest income earned on assets (like loans) and interest expense paid on liabilities (like deposits).
• Reserve requirements: Regulations on how much cash banks must hold relative to certain liabilities; these can affect how much they can lend.

If you’d like, I can tailor this explanation to a specific country, bank product (savings, checking, CDs), or provide a simple example with numbers.