Reviewed 11 August 2026 · Sourced from the CFPB, Regulation DD and the Federal Reserve
Compound interest is interest calculated on your original money and on the interest that money has already earned.
That is the entire idea, and everything else is arithmetic. It is also completely symmetrical: the same mechanism that turns steady saving into a number that surprises you is the one that makes a credit card balance grow while you are paying on it. Compounding does not care which direction it is pointed.
- Simple interest is paid on the principal only. Compound interest is paid on the principal plus everything already earned. Over one year they are nearly identical. Over thirty they are not remotely close.
- The formula is A = P(1 + r ÷ n) ^ (n × t). Time sits in the exponent, which is why years matter more than any other input you can control.
- Compounding frequency matters far less than people expect. At 5%, going from annual to daily compounding is worth about 0.13 of a percentage point.
- The Rule of 72 is an approximation, not a law. It is at its most accurate around 8% and gets steadily worse at both extremes — it is off by roughly 11% at a 36% rate.
- On debt, compounding runs in reverse. Federal Reserve data puts the average credit card rate on accounts assessed interest at 22.15%, and card interest is calculated daily.
- Inflation compounds too. A yield below the inflation rate is a balance that grows in dollars and shrinks in what those dollars buy.
What compound interest actually is
Interest is rent on money. Compound interest is what happens when you stop taking the rent out and let it sit there collecting rent of its own.
The Consumer Financial Protection Bureau puts it about as plainly as it can be put: compound interest is “when you earn interest on the money you've saved and on the interest you earn along the way.” Their example runs two years. Start with $1,000 at 5% annually. After year one you have $1,050 — the original thousand plus $50. After year two you have $1,102.50, because the second year's interest was calculated on $1,050 rather than on $1,000.
That extra $2.50 is the whole phenomenon. It looks like nothing. Two and a half dollars against a thousand is a rounding error, and if the story stopped in year two nobody would have built anything on it. What makes compounding worth a page is what that $2.50 becomes when it is allowed to do the same thing to itself, every year, for thirty years. It is not a big effect made bigger. It is a small effect applied to a growing base, which is a different shape of growth entirely.
The contrast that makes it legible is simple interest. Under simple interest, every year's interest is calculated on the original deposit and nothing else. $1,000 at 5% simple pays $50 in year one, $50 in year two, $50 in year forty. The base never moves. Under compound interest the base moves every single period, and each move makes the next one larger.
Almost everything a normal person holds compounds: savings accounts, money market accounts, CDs, retirement accounts, credit card balances. Simple interest shows up in specific places — some auto loans and personal loans accrue simple interest on the outstanding principal, and short-term instruments often quote it. When a product does not say, assume compound and read the disclosure to confirm.
The formula
One formula does the work, and a second one handles the case where you are adding money as you go — which for most people is the case that actually applies.
A = P ( 1 + r ÷ n ) ^ ( n × t )Where A is the amount you end up with · P is the principal you started with · r is the annual interest rate as a decimal (5% is 0.05) · n is how many times a year interest compounds · t is the number of years. To get the interest alone rather than the total, subtract P from A.
Put the simple-interest version beside it, because the difference between the two formulas is the difference between the two outcomes:
A = P ( 1 + r × t )Time is multiplied. In the compound formula, time is an exponent. That single structural difference is why the two curves separate the way they do.
Notice where t sits in each one. Multiplication produces a straight line. An exponent produces a curve that bends upward and keeps bending. It is the reason every honest explanation of compounding ends up saying the same unglamorous thing about starting early — not as encouragement, but because the exponent is where the leverage is, and the exponent is years.
If you are contributing every month rather than depositing once, you need the future value of a series:
FV = PMT × [ ( ( 1 + i ) ^ N − 1 ) ÷ i ]Where PMT is the amount you add each period · i is the interest rate per period (an annual rate divided by 12 for monthly contributions) · N is the total number of periods. Add the compound growth of any starting balance separately.
$500 a month, 30 years, an assumed 7% annual return compounding monthly. This is arithmetic on an assumption, not a prediction — no account is guaranteed to return 7%.
Roughly seventy percent of the ending balance is money you never deposited. That ratio, not the headline number, is the thing worth understanding — and it is entirely a function of how long the money was left alone.
Compounding frequency, and how much it really matters
Interest can compound annually, semiannually, quarterly, monthly, daily, or on any schedule an institution chooses. More frequent compounding produces a larger result, because the interest starts earning sooner. This is true, it is often oversold, and the size of the effect is easy to check.
The nominal rate is 5.00% in every row. Only the compounding frequency changes.
Worst to best: $12.67 on ten thousand dollars. Worth having. Not worth choosing a lower rate for. If one account compounds daily and another pays a quarter of a point more, take the quarter point without thinking about it.
There is a hard ceiling on this, which is a useful thing to know because it stops the “but what if it compounded even faster” question dead. As compounding periods approach infinity, the result converges on continuous compounding, which at 5% produces an effective 5.1271%. Daily compounding already delivers 5.1267%. The entire remaining distance between daily compounding and the mathematical limit is four ten-thousandths of a percentage point. There is nowhere left to go.
On the disclosure side, US law separates two things that sound like one. Regulation DD § 1030.4(b) requires a bank to tell you the frequency with which interest is compounded and the frequency with which it is credited — two separate disclosures, because they are often different. And § 1030.7 states outright that it “does not require institutions to compound or credit interest at any particular frequency.” The bank picks. It just has to tell you what it picked.
Because compounding frequency changes the outcome, a bare interest rate is not comparable across two accounts. APY — annual percentage yield — is the number that folds compounding in so the comparison works. If you are looking at a deposit account, the yield is the number to read; the rate underneath it is trivia.
What compounding does over time
Here is the same $10,000 at 5%, run two ways. The left column is simple interest, where only the original deposit ever earns. The right column is compound interest, annually.
| After | Simple interest | Compound interest | Difference |
|---|---|---|---|
| 1 year | $10,500.00 | $10,500.00 | $0.00 |
| 5 years | $12,500.00 | $12,762.82 | $262.82 |
| 10 years | $15,000.00 | $16,288.95 | $1,288.95 |
| 20 years | $20,000.00 | $26,532.98 | $6,532.98 |
| 30 years | $25,000.00 | $43,219.42 | $18,219.42 |
| 40 years | $30,000.00 | $70,399.89 | $40,399.89 |
Read down the difference column and the shape becomes obvious. Year one: nothing. Year five: $263, which is a nice dinner. Year ten: $1,289. Year forty: $40,400 — more than the entire simple-interest balance. The advantage is not growing steadily. It is accelerating, because each year's advantage is itself compounding.
This has an uncomfortable implication that gets left out of most explanations. Compounding is boring for a long time before it is impressive. Anyone starting from nothing will spend the first several years looking at a curve that appears flat, and being told to be patient by people who are further along it. That is not a character test and it is not a trick — it is the arithmetic doing exactly what it does. The early years feel like nothing because, in dollar terms, they are nearly nothing. They are also the years doing the most work, because they are the ones being compounded the longest.
The practical consequence: for the same total dollars, money added early beats money added later, and the gap widens with every year of delay. Not because of discipline or virtue. Because t is an exponent.
The Rule of 72
The Rule of 72 is a shortcut for estimating how long money takes to double at a given rate. Divide 72 by the rate, expressed as a whole number, and the answer is roughly the number of periods.
Years to double ≈ 72 ÷ rateWhere rate is the periodic compound rate written as a whole number, not a decimal — 6% is 6, not 0.06. At 6%, money doubles in roughly 12 years.
This is a rule of thumb, not a measured figure and not a law. It is a rounded convenience derived from the exact relationship, which uses natural logarithms:
Years to double = ln(2) ÷ ln( 1 + r )Where r is the rate as a decimal. This one is exact for a rate that compounds once per period and never changes.
72 is used instead of the mathematically cleaner 69.3 for one reason: it divides evenly by 2, 3, 4, 6, 8, 9 and 12, which is what you want in a number meant to be used without a calculator. Here is what that convenience costs, across the range of rates you actually meet.
| Rate | Rule of 72 | Exact | Error |
|---|---|---|---|
| 1% | 72.00 yrs | 69.66 yrs | +3.4% |
| 4% | 18.00 yrs | 17.67 yrs | +1.9% |
| 6% | 12.00 yrs | 11.90 yrs | +0.9% |
| 8% | 9.00 yrs | 9.01 yrs | −0.1% |
| 12% | 6.00 yrs | 6.12 yrs | −1.9% |
| 20% | 3.60 yrs | 3.80 yrs | −5.3% |
| 24% | 3.00 yrs | 3.22 yrs | −6.9% |
| 36% | 2.00 yrs | 2.25 yrs | −11.3% |
Where it breaks down
At very low rates it overstates the time. At 1% it says 72 years when the answer is 69.7. The error is small in percentage terms and enormous in years, which is a strange combination to hold in your head.
At high rates it understates the time, and the error grows fast. Past about 15% the rule starts telling you money doubles sooner than it does. At 36% it is wrong by more than eleven percent. This is the failure that costs something, because high rates are where debt lives.
It assumes the rate compounds once per period and never changes. Feed it a rate that moves, or one that compounds daily while you are thinking in years, and it answers a question you did not ask.
Card rates sit exactly in the band where the rule is least reliable, and the error runs in the direction that makes the debt look faster to escape than it is. Worse, the rule assumes nothing is being paid and nothing is being added — neither of which is true of a card you are actually using. For debt, do not estimate. Use the payoff arithmetic, or the calculator, and get the real number.
Compounding working against you
Every mechanism on this page runs in both directions. The formula does not know whether the balance is yours or the bank's, and none of the arithmetic changes sign when the money is owed instead of held.
The Federal Reserve's G.19 release of 7 August 2026 puts the average commercial-bank credit card rate for the second quarter of 2026 at 20.94% across all accounts and 22.15% on accounts actually assessed interest. That second figure is the one that describes someone carrying a balance.
And card interest does not wait for the month to end. The CFPB describes the mechanics: “Many credit card companies calculate the interest you owe daily, based on your average daily account balance,” at a rate they call the daily periodic rate. Because the interest is accruing daily, the CFPB notes, “the sooner you pay off all or some of your balance, the less interest you will pay.” At 22.15%, the daily periodic rate is 0.0607%. Held for a full year, daily compounding turns that 22.15% into an effective annual cost of 24.79%.
A $6,000 balance. No new charges. A fixed payment every month, with interest applied monthly at the annual rate divided by twelve. The first month's interest alone is $110.75, or about $3.64 a day.
The first extra $50 a month saves $2,172 and cuts two and a half years. The second $50 saves another $825. That is compounding read backwards: every dollar of principal you remove early is a dollar that never gets to grow against you, and the earliest dollars are the ones that would have grown the longest.
Two structural traps follow from the same mechanism.
Minimum payments are designed around it. A minimum payment is typically a small percentage of the balance plus that period's interest, so it clears very little principal — and each issuer sets its own formula, so the only reliable version is the one on your own statement. Regulation Z requires that statement to show you two things: how long the balance will take to pay off making only minimum payments, and the monthly payment that would clear it in 36 months. Those two lines are on the bill already. They are the most useful numbers the issuer prints and the ones most often skipped.
Unpaid interest can be added to principal. When accrued interest is capitalized — folded into the balance rather than paid — it starts generating interest of its own. This is how a balance grows during a period when nothing was borrowed. It appears in deferred-interest store financing, in some student loan situations, and anywhere a payment covers less than the interest that accrued. The rules differ by product, so the answer lives in your own paperwork, not in a general article.
A dollar that stops 22% compounding against you is worth more than a dollar earning 4% for you, and it is worth more with certainty rather than on an assumption. That is arithmetic, not advice — and it deliberately says nothing about your emergency fund, your employer match, or anything else about your situation. It is one comparison, and it is only one input.
The two things that quietly eat the return
Compound growth projections are almost always shown gross. Two forces work on the number afterward, and both of them compound as well.
Inflation
The Bureau of Labor Statistics reported the Consumer Price Index for All Urban Consumers up 3.5% over the twelve months ending June 2026. In the same window, the FDIC's deposit-weighted national rate for savings accounts was 0.38%.
Real return is roughly the nominal rate minus inflation. The precise version divides one by the other: (1 + rate) ÷ (1 + inflation) − 1.
A balance at the national average savings rate is growing in dollars and shrinking in what those dollars buy, by roughly three percent a year. Compounding is running; it is just running the wrong way. This is the strongest practical argument for checking what your account pays, and it has nothing to do with compounding frequency.
Taxes
In a regular taxable account, interest is income in the year it is earned. IRS Topic no. 403 lists interest on bank accounts, money market accounts and certificates of deposit as taxable, and states that “you must report all taxable and tax-exempt interest on your federal income tax return, even if you don't receive a Form 1099-INT.” A payer must issue that form once it has paid you at least $10 of reportable interest, but the obligation to report does not depend on the form arriving.
The compounding consequence is quiet. Tax paid on this year's interest is money that leaves the account, so it is not there to be compounded next year, or in any year after that. Over a long horizon, the drag is not the tax bill — it is everything the tax bill would have grown into. That difference is the entire structural argument for tax-advantaged accounts, and it is arithmetic rather than a recommendation about what anyone should hold.
Fees, which are the same shape
An annual fee expressed as a percentage — an expense ratio, an advisory fee, a monthly maintenance charge on a small balance — is charged on the balance every year, which means it compounds against you exactly the way interest compounds for you. A yield quoted before fees is not the yield.
What trips people up
- Treating a projection as a forecast. The formula tells you what happens if a rate holds for the whole period. No market rate holds for the whole period. Compound projections are arithmetic on an assumption, and the assumption is the fragile part.
- Comparing a nominal rate to a yield. The rate is before compounding; APY is after. Convert one or the other before deciding anything.
- Optimizing compounding frequency instead of the rate. At 5%, the whole annual-to-daily spread is about 0.13 of a point. The rate, the amount, and the years are where the money is.
- Using the Rule of 72 at high rates. It is tuned near 8% and understates doubling time badly above 15% — which is exactly the range credit card rates live in.
- Assuming a deposit rate is locked. Regulation DD exempts variable-rate accounts from its 30-day change notice, so a savings APY can move with no warning. A CD rate is fixed for its term; a savings rate is not fixed for anything.
- Forgetting it runs both directions. The same person can be compounding at 4% on $2,000 of savings and 22% on $6,000 of card debt, and describe themselves as saving.
- Quitting during the flat part. The first several years look like almost nothing because in dollar terms they are almost nothing. They are also the years being compounded the longest, which makes them the most valuable ones in the whole series.
Frequently asked questions
What is compound interest in simple terms?
It is interest that gets paid on your interest. The Consumer Financial Protection Bureau describes it as earning interest on the money you have saved and on the interest you earn along the way. Their example: $1,000 at 5% becomes $1,050 after one year, then $1,102.50 after two, because the second year is calculated on $1,050 instead of on the original $1,000. Simple interest, by contrast, would pay exactly $50 every year forever, because it only ever counts the original deposit.
What is the formula for compound interest?
A equals P times the quantity one plus r divided by n, raised to the power of n times t. A is the ending amount, P is the principal you started with, r is the annual rate written as a decimal, n is how many times a year the interest compounds, and t is the number of years. Subtract P from A to get the interest alone. The important detail is that time appears as an exponent rather than a multiplier, which is why the length of time you leave money alone matters more than any other input.
Does compounding daily instead of monthly make much difference?
Less than most people assume. On $10,000 at a 5% nominal rate, annual compounding produces $500 of interest in the first year and daily compounding produces $512.67. The entire spread is $12.67. Daily compounding is also very close to the mathematical ceiling: continuous compounding at that rate would yield 5.1271% against daily compounding's 5.1267%. Take the more frequent schedule if the rate is equal, but never accept a lower rate to get it.
How accurate is the Rule of 72?
It is an approximation, and its accuracy depends on the rate. It is nearly exact around 8%, where it says nine years and the true answer is 9.01. It drifts at both extremes. At 1% it says 72 years against a true 69.7. At 24% it says three years against a true 3.22, and at 36% it is off by more than eleven percent. It also assumes a constant rate compounding once per period, so it is unreliable for anything that moves.
How does compound interest work against you on debt?
Identically, just pointed the other way. Interest is added to your balance, and the next round of interest is calculated on the larger balance. Credit card interest is typically calculated daily on your average daily balance, so it compounds every day. The Federal Reserve reported an average rate of 22.15% on card accounts assessed interest in the second quarter of 2026. Held for a full year with daily compounding, that works out to an effective annual cost of about 24.79%.
Does inflation cancel out compound interest?
It offsets part of it, and sometimes more than all of it. Compound growth is measured in dollars, while inflation measures what those dollars buy. The Bureau of Labor Statistics reported consumer prices up 3.5% over the twelve months ending June 2026, while the FDIC national rate for savings accounts was 0.38%. A balance earning 0.38% while prices rise 3.5% loses roughly 3% of its purchasing power in a year, even though the dollar figure on the statement went up.
Related terms
Where to go next
- Run your own numbers in the compound interest calculator or the investment growth calculator — both free, no account.
- See the same math pointed at a balance you owe with the debt payoff calculator, then read avalanche vs snowball.
- Build the balance that does the compounding: emergency fund calculator and how to save your first $1,000.
- Work through Stage 2 · Stabilize for the debt side and Stage 4 · Invest for the long horizon.
- Browse every definition in Learn the Lingo.
- Consumer Financial Protection Bureau, How does compound interest work? (definition and the $1,000 at 5% two-year example).
- Consumer Financial Protection Bureau, How is my credit card interest calculated? (daily periodic rate, average daily balance, daily accrual).
- Board of Governors of the Federal Reserve System, Consumer Credit — G.19, released 7 August 2026: commercial bank credit card plans, Q2 2026 — 20.94% on all accounts, 22.15% on accounts assessed interest.
- Consumer Financial Protection Bureau, Regulation DD § 1030.4 — Account disclosures (compounding and crediting frequency must both be disclosed).
- Consumer Financial Protection Bureau, § 1030.7 — Payment of interest (no required compounding frequency; daily balance and average daily balance methods).
- Consumer Financial Protection Bureau, § 1030.5 — Subsequent disclosures (30-day advance notice, and the variable-rate exemption).
- Consumer Financial Protection Bureau, Regulation Z § 1026.7(b)(12) — Repayment disclosures (the minimum-payment payoff estimate and the 36-month payment figure required on card statements).
- U.S. Bureau of Labor Statistics, Consumer Price Index news release, released 14 July 2026: CPI-U up 3.5% over the 12 months ending June 2026.
- Federal Deposit Insurance Corporation, via Federal Reserve Bank of St. Louis, National Rate: Savings (SNDR) — 0.38%, July 2026.
- Internal Revenue Service, Topic no. 403, Interest received, and Instructions for Forms 1099-INT and 1099-OID ($10 filing threshold; obligation to report all taxable interest).
The figures on this page are checked against the source that publishes them, and dated. Published rates move after the release named above — the linked source always carries the current number. This page explains a term; it does not recommend a product.