Start with one deposit and no other movements

Take a hypothetical deposit of 500 earning four per cent annually, with interest added at the end of each year. Assume the rate remains unchanged and there are no deposits, withdrawals, fees or taxes. These assumptions make the arithmetic visible; they do not describe an available account or predict a return.

After one year, interest is 500 times 0.04, or 20. The balance becomes 520. During the second year, four per cent is applied to 520, producing 20.80. The final balance is 540.80. The extra 0.80 arises because the first year's 20 also earns interest.

Compare with interest paid away

If the same 20 of annual interest were paid out and the original 500 remained unchanged, two years would produce 40 of interest outside the account. The combined amount would be 540, before considering what happened to those payments. The difference from 540.80 is small in this short example but explains the mechanism.

The compound calculation can be written as 500 multiplied by 1.04 twice. For an unchanged annual rate over n years, the expression is starting amount multiplied by (1 plus rate) to the power n. The rate is written as a decimal, so four per cent becomes 0.04.

Separate contributions from interest

Adding new money increases the balance for a different reason. If an additional 100 is deposited after the first year's interest, the second year starts at 620 and earns 24.80 under the same simplified assumption. The final 644.80 contains 600 of contributions and 44.80 of interest. Calling the whole increase an investment return would confuse saving with growth.

Different compounding schedules produce different calculations, and a variable rate cannot be represented accurately by repeating one unchanged rate. Account illustrations also depend on when deposits and withdrawals occur. US APY disclosure rules explicitly address annualised yield assumptions; real statements should be checked against the relevant provider's terms.

Use the example to understand why leaving interest in place changes the next calculation. Do not turn it into a promise that money will follow a smooth path indefinitely. Inflation, tax, fees and changing rates affect the usefulness of the final amount, while investment returns can involve losses as well as gains.