Compound interest

What It Means

Compound interestInterest rateThe yearly percentage a lender charges for borrowing money, not counting fees; the APR adds certain fees to show a fuller cost. See more is interest paid on the original amount and on the interest that amount has already earned. Each time interest is added to the balance, the next round is worked out on the bigger total, so the dollars earned grow year after year even at the same rate. Investor.gov, run by the SEC, sums it up as interest you earn on interest.

How It Sounds at Home

• "Leave it alone and let it compound."
• "The interest is starting to earn its own interest."
• "Compounding does the heavy lifting over twenty years."

The Breakdown

Formula. Balance = deposit × (1 + rate ÷ n)^(n × years), where n is how many times a year interest is added.

Worked example. $5,000 at an example 5% a year, compounded yearly, with nothing more added:

What the result means. In the first few years compound and simple interest look almost the same. The gap widens with time, because every year's interest is added to the balance that earns the next year's. On money you owe, compounding works the same way against you.

How often it compounds. The same $5,000 at 5% for 10 years comes to $8,235 compounded monthly and $8,243 compounded daily, against $8,144 compounded yearly. For a deposit account, the APYAPYA yearly rate showing the total interest a deposit account pays, counting how often interest compounds, as defined by federal Truth in Savings rules. See more already counts the compounding, so compare APYs rather than base rates.

Good to Know

Investor.gov, run by the SEC, has a free compound interest calculator where you can change the rate, the time and how often interest compounds. For a savings accountSavings accountA bank or credit union account for money you're setting aside for later, which earns interest and is insured up to federal limits at insured institutions. See more or CDCertificate of depositA deposit you agree to leave at a bank or credit union for a set term, until its maturity date, usually with a penalty for taking money out early. See more, compare the APY, because Regulation DD (12 CFR 1030.2) builds the frequency of compounding into it. Long projections assume one rate for every year; real account rates change and investment returns rise and fall, so treat a 30-year figure as an illustration. No return is guaranteed.

Related Terms and Categories

• Simple interest

  Interest figured only on the principal, never on interest already earned, so the same balance at the same rate adds the same amount each period.

• APY

  A yearly rate showing the total interest a deposit account pays, counting how often interest compounds, as defined by federal Truth in Savings rules.

• Rule of 72

  A shortcut for how many years money takes to double at a steady compound rate: divide 72 by the yearly rate, so 6% doubles in about 12 years.

• Savings account

  A bank or credit union account for money you're setting aside for later, which earns interest and is insured up to federal limits at insured institutions.

• Certificate of deposit

  A deposit you agree to leave at a bank or credit union for a set term, until its maturity date, usually with a penalty for taking money out early.

• Interest rate

  The yearly percentage a lender charges for borrowing money, not counting fees; the APR adds certain fees to show a fuller cost.

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