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1Fix the driver behind crashes, sound loss and screen glitches2Clear out junk files and repair common Windows errors3Scan for outdated or missing drivers - takes under a minuteCompound interest is interest earned on your original amount and on the interest that has already been added to it. Each period’s interest becomes part of the balance that earns interest in later periods, so growth accelerates over time rather than staying flat. The same mechanism works against you on debt when unpaid interest is added to the balance.
How compound interest works, step by step
The Consumer Financial Protection Bureau (CFPB) defines compound interest as earning interest “on the money you’ve saved and on the interest you earn along the way.” Investor.gov, the U.S. Securities and Exchange Commission’s investor education site, gives a shorter glossary version: interest paid on principal and on accumulated interest. Both describe the same idea.
Take a concrete case. You deposit $1,000 in an account that pays 5% a year, and interest is added once a year:
| End of year | Starting balance | Interest earned that year | Ending balance |
|---|---|---|---|
| Year 1 | $1,000.00 | $50.00 (5% of $1,000) | $1,050.00 |
| Year 2 | $1,050.00 | $52.50 (5% of $1,050) | $1,102.50 |
| Year 3 | $1,102.50 | $55.13 (5% of $1,102.50, rounded) | $1,157.63 |
The CFPB uses the same $1,000 at 5% example, with a balance of $1,050 after year one and $1,102.50 after year two. The second year earns $52.50 rather than $50 because that year’s interest is calculated on $1,050, which includes the first year’s $50. The gap is small at first, which is why compounding is easy to underestimate.
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Simple interest is calculated only on the original principal. Over two years, $1,000 at 5% simple interest earns $50 a year, for a total of $100 and a balance of $1,100. Compounded annually at the same rate, the balance is $1,102.50. The $2.50 difference is the interest-on-interest. It grows with larger balances, longer periods and higher rates.
Whether an account actually credits simple or compound interest depends on its terms. Check the account’s disclosure for how and when interest is added, rather than assuming.
The formula and what its inputs mean
For a fixed annual rate compounded a fixed number of times per year, the standard future-value formula is:
A = P(1 + r/n)nt
- P is the starting principal.
- r is the annual interest rate written as a decimal (5% becomes 0.05).
- n is the number of compounding periods per year (1 for annual, 12 for monthly, 365 for daily).
- t is the number of years.
- A is the balance at the end of the period.
The formula assumes the rate and compounding schedule stay fixed and that you make no deposits or withdrawals. It is a teaching model. It does not describe a specific account, and it is not a payoff calculator for a loan, where fees, minimum payments and changing rates all matter.
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Why compounding frequency matters, and how APY fixes the comparison
Holding the nominal rate constant, more frequent compounding produces a slightly higher balance. Using the formula with a 5% nominal rate:
| Compounding schedule | Effective annual return on $1,000 (worked arithmetic) |
|---|---|
| Annually (n = 1) | 5.00%, balance $1,050.00 |
| Monthly (n = 12) | About 5.12%, balance about $1,051.16 |
| Daily (n = 365) | About 5.13%, balance about $1,051.27 |
These are arithmetic results for the stated rate, not offers from any institution. The difference is modest, and it does not mean a monthly account is better than an annual one. A higher nominal rate with less frequent compounding can beat a lower rate that compounds daily.
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That is why savings products are compared on annual percentage yield (APY). Under the CFPB’s Regulation DD Appendix A, APY annualizes the interest earned relative to principal and the number of days in the term. The CFPB’s worked example takes a $1,000 deposit that earns $61.68 over a 365-day term and calculates a 6.17% APY. That example illustrates the formula only; it is not an advertised account rate. The regulatory calculation assumes principal and interest stay on deposit for the term with no other transactions. Real results change if you withdraw money, add funds, pay fees, or if the rate changes.
Growth over longer periods
Investor.gov illustrates the effect with $100 at 5% a year, which grows to more than $162 after 10 years and almost $340 after 25 years. Those figures assume the stated rate holds for the entire period. They are educational illustrations, not forecasts. Investor.gov’s publication date for this page was not shown when it was accessed.
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One free scan finds every outdated or missing driver and matches the right update for your exact hardware.Free scan · exact hardware matchThe lesson is in the shape of the curve. Growth is slow at the start and faster later, so the amount of time an account stays invested often matters more than any single period’s rate.
The Rule of 72: a quick estimate
To estimate how long money takes to double at a steady annual rate, divide 72 by the rate expressed as a whole number. At 9%, 72 ÷ 9 = 8, so the balance doubles in about 8 years. Investor.gov presents this rule as an approximation that assumes a steady rate. It is useful for mental math, but it is not exact. Rates above roughly 2% to 3% give the most useful estimates; at very low rates, the error grows.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.Compound interest on debt
The same mechanics apply to debt. If interest is charged on an unpaid balance and then added to that balance, the interest you owe starts to accrue on the interest. Credit cards are the most common example. Investor.gov advises paying attention to high-interest credit-card debt for this reason.
Your actual cost depends on the loan contract: the rate, how often interest is charged, your payments, and any fees. A fixed-rate formula cannot tell you your payoff date or total cost. Use your lender’s disclosures or statement figures for that.
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Savings and investments are not the same
A bank savings account’s interest is set by the institution and disclosed as APY. Investment growth is different. Investor.gov’s introduction to investing states that investments involve risk and do not have a set rate of return. Illustrations of investment growth rest on assumptions about contributions, time, fees and returns, and actual results can be lower than the illustration, including losses. Do not treat an investment projection as equivalent to a guaranteed savings return.
What to check when comparing accounts
- The disclosed APY, which allows like-for-like comparison.
- The nominal rate and how often interest is compounded and credited.
- Whether the rate can change after you open the account.
- Term length, early-withdrawal penalties and minimum balance requirements.
- Fees that reduce the balance.
- The balance and deposit assumptions behind the stated APY.
For investment illustrations, check the contribution amount, the holding period, the assumed rate of return and the fees. Investor.gov’s free online compound-interest calculator lets you test these assumptions yourself, and the CFPB points readers to the same tool.
Compound interest rewards time and consistency. Used on savings, it adds up slowly and steadily; used on debt, it adds up against you. Knowing which side of the balance you are on tells you how much the schedule and the rate matter.
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