How interest on interest changes a savings balance

Imagine setting aside $800 for three years at a constant annual interest rate of 4%, with no deposits, withdrawals or fees. The first year earns $32 either way. If interest stays in the balance and the next year’s interest is calculated on that larger balance, the paths begin to diverge.

Start with the same first year

The amount you start with is the principal. Four percent of $800 is $32, so the account ends the first year at $832. The Consumer Financial Protection Bureau describes compound interest as earning interest on both the starting money and interest earned along the way.

In year two, use $832 as the starting balance. Multiply by 1.04 to get $865.28. In year three, multiply $865.28 by 1.04 to get about $899.89. The amount earned each year increases because the base increases.

Compare with interest on the starting amount

If the calculation paid a fixed $32 each year on the original $800 alone, three years would produce $96 and an ending amount of $896. Annual compounding adds about $3.89 in this example. The difference is small at first and grows as more periods of interest build up.

Extend both invented scenarios to ten years, with the same assumptions. At $32 a year, interest totals $320 and the original principal plus interest is $1,120. With annual compounding, $800 multiplied by 1.04 ten times is about $1,184.20. The larger difference reflects ten rounds of growth on an increasing balance.

Read the terms behind a quote

The SEC’s educational example demonstrates how repeated compounding changes a balance over time. An actual account can have a changing interest rate, fees, restrictions and different compounding or crediting schedules. Before comparing offers, line up the time horizon and check whether the figures describe annual yield or an interest rate stated on another basis. If an annual yield already incorporates compounding, use that definition when comparing.

Additional deposits and withdrawals change how much money earns interest and for how long. To isolate the effect of a rate, compare like balances and dates. To estimate what your savings might do in practice, put the expected movements into the calculation.