How to Calculate Compound Interest (Formula + Examples)

Compound interest is interest paid on the interest you have already earned, as well as on the money you started with. The formula is A = P × (1 + r/n)^(n × t), and 10,000 left at 5% a year compounded yearly for 10 years grows to 16,288.95 — 6,288.95 of interest, against 5,000 if the interest never compounded.

The quickest route here: the Compound interest calculator takes the starting amount, the annual rate, the number of years, the compounding frequency and an optional regular contribution, and returns the final amount, the total you put in, the interest earned and a year-by-year table. Everything is computed on your device. This guide is general information about the arithmetic, not financial advice.

The formula, term by term

A = P × (1 + r/n)^(n × t)

• A — the final amount
• P — the principal, what you start with
• r — the annual rate as a decimal: 5% is 0.05, not 5
• n — how many times interest is added per year: 1 yearly, 2 half-yearly, 4 quarterly, 12 monthly, 365 daily
• t — the number of years

Interest earned is A − P. The mechanism is the exponent: each period's interest joins the balance and earns interest itself from then on. Simple interest does not do that — it always applies the rate to the original 10,000, giving 500 a year, 5,000 over a decade and a final 15,000. The 1,288.95 difference is the compounding.

Reference table: what the frequency is worth

10,000 at 5% a year for 10 years, changing only how often interest is added:

Compounding	n	Final amount	Interest	Effective annual rate
Yearly	1	16,288.95	6,288.95	5.0000%
Half-yearly	2	16,386.16	6,386.16	5.0625%
Quarterly	4	16,436.19	6,436.19	5.0945%
Monthly	12	16,470.09	6,470.09	5.1162%
Daily	365	16,486.65	6,486.65	5.1267%

Frequency matters, but with diminishing returns. Going from yearly to monthly adds 181.15 over ten years; going from monthly to daily adds another 16.55. There is a ceiling — continuous compounding — and daily is already almost on it.

APR, APY and TAEG

Those last two columns are the reason two products quoting "5%" are not the same product.

• The nominal annual rate, often labelled APR, is the periodic rate multiplied by the number of periods. 5% compounded monthly means 0.05 ÷ 12 per month.
• The effective annual rate, labelled APY on savings or TAEG on credit in French-speaking markets, is what one year actually costs or earns once compounding is counted: (1 + r/n)^n − 1.

Nominal rate	Compounded	Effective annual rate
3%	monthly	3.0416%
5%	monthly	5.1162%
10%	monthly	10.4713%
20%	monthly	21.9391%

The gap widens with the rate, which is why it is most visible on credit cards and overdrafts. On borrowing, the effective figure is usually the one that also folds in compulsory fees, so it is the number to compare offers on. For a loan with a repayment schedule, see how loan interest works.

Adding money every month

Most people are not leaving a lump sum alone; they are paying in. Contributions compound too, and the total is the sum of two pieces: the original amount growing on its own, plus the future value of the payment stream.

FV of the contributions = PMT × [((1 + i)^N − 1) ÷ i], where i is the rate per period (r/n) and N is the number of periods (n × t).

Worked through with 10,000 at 5% compounded monthly, plus 200 at the end of every month for 10 years:

• i = 0.05 ÷ 12, N = 120
• The 10,000 alone becomes 16,470.09
• The contributions become 200 × [((1 + 0.05/12)^120 − 1) ÷ (0.05/12)] = 31,056.46, on 24,000 paid in
• Final amount: 47,526.55, of which 34,000 is your own money and 13,526.55 is interest

Paying at the start of each month instead multiplies the annuity part by (1 + i) and gives 47,655.95 — 129.40 more, for the same money moved a few weeks earlier. Note that the contributions did most of the work here: they added 31,056.46 to a balance that would otherwise have reached 16,470.09.

What the formula assumes

• A constant rate. Real savings rates move and real investment returns swing from year to year and can be negative. The formula draws a smooth curve through something that is not smooth.
• Nothing is taken out. Fees, account charges and tax on interest or gains all reduce the rate you actually compound at. Tax treatment depends on your country and your situation, so the numbers above are before both.
• Money keeps its value. It does not, which is the next section.
• Past returns are not a prediction. A figure you put in the rate box is an assumption you have chosen, not a forecast. Nothing here promises a return.

Inflation, or what the number is worth

A future amount is not today's money. If prices rise 2% a year, ten years multiply them by 1.02^10 = 1.2190, a rise of about 22%. The 47,526.55 above would then buy roughly what 38,988.33 buys today.

The real rate is not the difference between the two rates but the ratio: (1 + rate) ÷ (1 + inflation) − 1, here 1.05 ÷ 1.02 − 1 = 2.94% a year, slightly below the 3% the subtraction suggests. The Inflation calculator converts amounts between years, and the Investment calculator projects contributions and shows the result in today's money.

The rule of 72

To estimate how long money takes to double, divide 72 by the rate in percent. At 6%: 72 ÷ 6 = 12 years, against an exact 11.90. At 8%: 9 years, against an exact 9.01. It is tightest around 8% and loosens either side — at 3% it says 24 years where the answer is 23.45, and at 12% it says 6 where the answer is 6.12. Good enough for a conversation, not for a plan.

Common problems, and what they mean

The result is astronomically large. The rate went in as 5 instead of 0.05. Check that r is a decimal.

Monthly compounding gives less than yearly. The rate was divided by 12 but the years were not multiplied by 12, or the reverse. Both changes belong together: i = r/n and N = n × t.

Your bank's statement does not match your calculation. You have probably used the nominal rate where the bank quotes the effective one, or interest is credited on a schedule — quarterly, or at the end of a term — rather than continuously.

A contribution model is off by one payment. Payments at the start of a period earn one extra period of interest. Pick beginning or end of period deliberately.

The projection looks great but the real gain is small. Inflation, fees and tax have not been taken out. Convert the final amount into today's money before deciding anything.

Questions people ask

What is the difference from simple interest? Simple interest always applies the rate to the starting amount. Over 10 years at 5%, 10,000 earns 5,000 simple, or 6,288.95 compounded yearly.

Which compounding frequency should I assume? The one in the contract. If it is not stated, compare products on their effective annual rate instead.

Does this work for debt? The same arithmetic runs in the other direction, which is why an unpaid credit card balance grows quickly. Repayments make it a loan calculation rather than a pure compounding one.

Can I solve for the rate or the time? Yes, by rearranging: t = ln(A/P) ÷ (n × ln(1 + r/n)). The calculator is quicker.

Is a projection a promise? No. It shows what a chosen rate would produce if it held every year, which no market does.

Next steps

• Project regular saving and see it in today's money: Investment calculator
• Compare with interest that never compounds: Simple interest calculator
• See what inflation does to an amount over time: Inflation calculator