Compound Interest vs APY

Compounding is a process; APY is an annual comparison

Compounding means interest can earn further interest after it is credited to the balance. An annual nominal rate tells you the stated rate before accounting for the chosen compounding frequency. Annual percentage yield, or APY, expresses an annualized yield that reflects compounding under the account's disclosed assumptions.

The CFPB introduces compound interest, while Regulation DD's APY calculation appendix sets out deposit-disclosure calculations. Account terms, term length, and rate structure matter; a basic fixed-rate formula is a teaching model rather than a substitute for the bank's disclosure.

Worked example: a nominal 6% rate

Suppose $10,000 earns a fixed nominal 6% annual rate with monthly compounding, no fees, and no additional deposits. Each monthly period uses 0.06 ÷ 12 = 0.005. After one year:

The effective annual rate is about 6.1678%, so interest is $616.78. At annual compounding, the same nominal 6% produces $10,600. The difference is $16.78 on this balance over this year. More frequent compounding can help at a positive fixed nominal rate, but it should not distract from larger differences in rates, fees, or contribution amounts.

For a nominal annual rate r and m equal compounding periods per year, the effective annual rate is (1 + r/m)^m − 1. For continuous compounding, the tool uses e^r − 1. Those formulas assume the rate remains constant.

Avoid compounding an APY twice

If an account advertises a 6% APY, entering 6% as a nominal rate with monthly compounding produces a higher yield than the advertised APY. For a simple constant-rate projection, select annual compounding and enter 6%, or convert the APY to an equivalent monthly-compounded nominal rate.

With APY expressed as 0.06, the equivalent nominal rate is about 5.8411%. Both approaches produce $10,600 after a full year with no deposits. Actual daily accrual, statement periods, and changing balances may differ from this mathematical equivalence.

Recurring deposits change the story

Use $10,000 initially, a nominal 6% rate, monthly compounding, one year, and $200 contributed monthly. This tool places contributions at the end of each contribution period. The resulting balance is about $13,083.89: $12,400 of your money and $683.89 of modeled interest.

The first $200 deposit earns for 11 months; the final deposit earns for zero months. That is why multiplying the full $12,400 by a one-year yield overstates the result. Beginning-of-month deposits would earn slightly more, but that is not this tool's convention.

The calculator evaluates each deposit at its own time and includes only completed contribution periods. For a fractional-year horizon, check the number of deposits rather than assuming a partial contribution is made at the end.

Reading results and avoiding common mistakes

• Projected balance includes your starting money, deposits, and modeled interest. It is not all investment profit.
• Interest earned subtracts starting principal and contributions from the ending balance.
• Effective rate reflects compounding for one year; it is not your personal return on deposits arriving throughout the year.
• Growth multiple should be read with its stated denominator. New deposits can increase the ending balance without representing investment performance.

A common error is treating a smooth fixed-rate projection as a forecast for stocks or other volatile assets. Another is comparing balances before tax with future spending in today's purchasing power. Neither taxes nor inflation is removed by this calculator.

Assumptions, limitations, and sources

The model uses a constant nonnegative nominal rate, the selected compounding frequency, and end-of-period deposits. It excludes withdrawals, fees, taxes, inflation, and variable returns. It clamps negative rate inputs to zero, so it cannot stress-test investment losses. Continuous compounding is a mathematical option, not a promise about an available savings account.

Compare alternative rates and contribution amounts, then check the actual account's APY, fees, withdrawal rules, and rate-change terms. The linked CFPB resources ground the definitions; all numerical examples here were calculated independently using the stated assumptions.