What is the formula for compound interest?

For a lump sum, A = P(1 + r ÷ n)^(n·t), where P is the starting balance, r the nominal annual rate, n the number of compounding periods a year and t the years. With regular deposits added, there is no single tidy expression, which is why this calculator runs the balance month by month instead, it handles both cases with the same code.

Does compounding frequency really matter?

Less than people expect, and it is bounded. Going from annual to daily compounding at 7% raises the effective rate from 7.000% to 7.250%, worth having, but small next to the effect of the rate itself or the length of time. What it does matter for is comparing accounts: always compare effective annual rates, never quoted ones.

What is the difference between APR and APY?

APY is the effective annual rate, it already includes compounding, which is why savings accounts advertise it. APR is the nominal rate and does not, which is why loans quote that instead. This calculator asks for the nominal rate and shows you the effective one it works out to.

How long does it take to double my money?

Divide 72 by the rate as a whole number for a quick estimate, at 7%, about 10.3 years. The rule of 72 is an approximation that works well between about 5% and 12%. To get the exact figure, set the monthly deposit to zero here and adjust the years until the balance doubles. To solve for a deposit rather than a balance, use the savings goal calculator.

Should I use my expected investment return here?

You can, but read the result carefully. A constant 7% is a reasonable long-run average for a diversified equity portfolio before inflation, and a badly misleading description of any individual decade. For a retirement horizon specifically, the retirement calculator adds the withdrawal tax this one leaves out. A smooth curve says nothing about the range of outcomes around it, and this model has no way to show you that range.

Are these figures before or after tax and inflation?

Before both. If the account is taxable, gains are reduced by tax in the year they are earned or realised. And inflation means the final balance buys less than the same number of dollars does today, at 3% inflation, money loses roughly half its purchasing power over 24 years, which the inflation calculator puts a figure on.

Compound Interest Calculator

This compound interest calculator shows what a balance grows to with regular deposits at any compounding frequency. It also shows the effective annual rate you actually earn, which is not the rate you were quoted, and how much of the final balance you never deposited.

Example numbers

The answerfrom an example

This grows to $106,639, of which $36,639 is interest you never deposited.

Worked on $10,000 to start, $500 a month, 7% compounded monthly for 10 years. Change anything below to use yours.

Final balance: $106,639
Total you paid in: $70,000
Interest earned: $36,639

The figures behind it

Final balance: $106,639; After 10 years.
Total you paid in: $70,000; Starting balance plus every deposit.
Interest earned: $36,639; 34.4% of the final balance was never deposited by you.
Effective annual rate: 7.229%; A nominal 7.00% compounded monthly is worth this much over a year.
Growth multiple: 1.52x; Final balance divided by what you put in.

Final balance$106,639

56%

34%

Starting balance$10,000
Deposits you made$60,000
Interest earnedMoney the money made.$36,639

The balance against what you put in

Years from today

BalanceWhat you put in

Payment scheduleShow

The table scrolls sideways

Year	Monthly in	Paid in to date	Growth to date	Balance
1	$500	$16,000	$919	$16,919
2	$500	$22,000	$2,339	$24,339
3	$500	$28,000	$4,294	$32,294
4	$500	$34,000	$6,825	$40,825
5	$500	$40,000	$9,973	$49,973
6	$500	$46,000	$13,782	$59,782
7	$500	$52,000	$18,299	$70,299
8	$500	$58,000	$23,578	$81,578
9	$500	$64,000	$29,671	$93,671
10	$500	$70,000	$36,639	$106,639

What this result assumes

A nominal 7.00% compounded monthly works out at 7.229% a year. That figure, not the quoted one, is what actually grows the balance.
Deposits are made at the end of each month, so a deposit earns nothing in the month it is made. This is the more conservative convention and the more common one.
The rate is held constant for the whole period. No real investment behaves this way, and a smooth curve tells you nothing about the range of outcomes around it.
Tax, fees and inflation are all excluded. Every figure is nominal and pre-tax.

Methodology

Reviewed August 31, 2026

Compounding frequency, and why the quoted rate is not the rate

A nominal annual rate is not what you earn unless it is compounded exactly once a year. Compounded n times a year, a nominal rate r is worth (1 + r ÷ n)ⁿ − 1 over the year. At 7%, that is 7% compounded annually, 7.186% quarterly, 7.229% monthly and 7.250% daily — the last of which is within a basis point of continuous compounding, e⁰·⁰⁷ − 1.

This calculator converts whatever frequency you choose into an equivalent monthly rate, (1 + effective)^(1/12) − 1, and then runs the schedule monthly. That is what lets daily compounding and monthly deposits coexist in one model without either being approximated away.

The effective annual rate is shown as its own figure because it is the honest basis for comparing two accounts. A 7.10% rate compounded annually beats a 7.00% rate compounded daily; the quoted numbers say the opposite.

When the deposit lands

A deposit made at the start of a month earns interest for that month; one made at the end does not. Over ten years and 120 deposits that is not a rounding difference — it is one extra period of growth on every contribution.

End-of-month is the default because it is the more conservative assumption and the one most savings products actually follow. The finance term for the other convention is an annuity-due, and if your deposits come out on payday at the start of the month, that is the one to pick.

The figure that matters

The result worth looking at is not the final balance but the split between what you paid in and what the interest earned. Early on, essentially all of the balance is your own money. The point at which growth overtakes contributions is the whole argument for starting early, and it is visible on the chart as the moment the two lines separate for good.

Money is held in whole cents throughout and interest is rounded to the cent each month, so a 70-year schedule cannot accumulate floating-point drift. The test suite checks the lump-sum case against the closed-form A = P(1 + r)ᵗ.

Assumptions

The interest rate is constant for the whole period. No real investment behaves this way.
Deposits are the same every month, and are made either all at the start or all at the end.
Interest is credited at the frequency chosen and never withdrawn.
Tax on interest or gains is excluded. Every figure is pre-tax.
Inflation is ignored, so the final balance is in nominal dollars and buys less than the same figure does today.
Account fees, fund expense ratios and transaction costs are excluded.
No withdrawals are made, and no deposit is ever missed.

Sources

Common questions

What is the formula for compound interest?: For a lump sum, A = P(1 + r ÷ n)^(n·t), where P is the starting balance, r the nominal annual rate, n the number of compounding periods a year and t the years. With regular deposits added, there is no single tidy expression, which is why this calculator runs the balance month by month instead, it handles both cases with the same code.
Does compounding frequency really matter?: Less than people expect, and it is bounded. Going from annual to daily compounding at 7% raises the effective rate from 7.000% to 7.250%, worth having, but small next to the effect of the rate itself or the length of time. What it does matter for is comparing accounts: always compare effective annual rates, never quoted ones.
What is the difference between APR and APY?: APY is the effective annual rate, it already includes compounding, which is why savings accounts advertise it. APR is the nominal rate and does not, which is why loans quote that instead. This calculator asks for the nominal rate and shows you the effective one it works out to.
How long does it take to double my money?: Divide 72 by the rate as a whole number for a quick estimate, at 7%, about 10.3 years. The rule of 72 is an approximation that works well between about 5% and 12%. To get the exact figure, set the monthly deposit to zero here and adjust the years until the balance doubles. To solve for a deposit rather than a balance, use the savings goal calculator.
Should I use my expected investment return here?: You can, but read the result carefully. A constant 7% is a reasonable long-run average for a diversified equity portfolio before inflation, and a badly misleading description of any individual decade. For a retirement horizon specifically, the retirement calculator adds the withdrawal tax this one leaves out. A smooth curve says nothing about the range of outcomes around it, and this model has no way to show you that range.
Are these figures before or after tax and inflation?: Before both. If the account is taxable, gains are reduced by tax in the year they are earned or realised. And inflation means the final balance buys less than the same number of dollars does today, at 3% inflation, money loses roughly half its purchasing power over 24 years, which the inflation calculator puts a figure on.

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