How Compound Interest Works (With Examples You Can Check)

By the SAA Tool editor, an IT support engineer · Last reviewed 1 October 2026 · 5 min read

Compound interest means earning interest on your interest. Each time interest is added to your balance, the next lot is worked out on the bigger total, so growth speeds up the longer you leave the money alone. The same maths works against you on debt. This guide explains the formula, why compounding frequency matters less than you might think, and what really drives growth, with worked examples you can check on any calculator.

Simple interest vs compound interest

With simple interest, you only ever earn interest on the amount you started with. 10,000 at 5% a year for 3 years earns 10,000 × 0.05 × 3 = 1,500.

With compound interest, each year's interest joins the balance:

That's 1,576.25 of interest instead of 1,500. The gap is small at first and grows every year. The US SEC's Investor.gov uses the same idea with $100 at 5%: $105 after one year, $110.25 after two, over $162 after 10 years and nearly $340 after 25.

The formula

Final amount = P × (1 + r ÷ n)^(n × t)

• P is the starting amount.
• r is the yearly interest rate as a decimal, so 4% is 0.04.
• n is how many times a year interest is added: 1 for yearly, 12 for monthly.
• t is the number of years.

Example: €5,000 at 4% a year, compounded monthly, for 10 years is 5,000 × (1 + 0.04 ÷ 12)^120 = €7,454.16.

You can test the formula against Australia's Moneysmart, which says A$10,000 at 3% compounded monthly grows to A$11,616 after 5 years, A$13,494 after 10 and A$18,208 after 20. Put those numbers into the formula and you get the same results, rounded to the dollar.

How often interest is added

More frequent compounding adds interest to the balance sooner, so it earns a little more. Here is 10,000 at 6% for 10 years:

Moving from yearly to monthly is worth something; moving from monthly to daily adds just 26.32 over ten years.

The last column is the effective yearly rate, which banks show so you can compare accounts that compound differently. In the UK it's called the AER, and in the US the APY:

Effective rate = (1 + r ÷ n)^n − 1

US rules give a worked example you can check in the Regulation DD formula: $61.68 of interest in a year on $1,000 is an APY of 6.17%. That's exactly what 6% compounded monthly produces, since 1,000 × ((1 + 0.06 ÷ 12)^12 − 1) = 61.68. When comparing savings accounts, compare the effective rates rather than the headline ones.

Adding money regularly

For most savers, regular deposits and time matter far more than compounding frequency. Start with 10,000, add 200 at the end of every month, and earn 6% a year compounded monthly for 10 years, and you end up with 50,969.84. You paid in 34,000, so 16,969.84 is interest. Paying in at the start of each month instead gives 51,133.72, because each deposit earns one extra month.

Time does the heavy lifting. Saving 200 a month at 6%, with nothing to start:

After 30 years, interest makes up about 64% of the balance. In rupees, ₹5,000 a month for 15 years at 7% grows to about ₹1,584,811, from ₹900,000 paid in.

The rule of 72

To estimate how long money takes to double, divide 72 by the yearly rate. Investor.gov's example: at 9%, money doubles in about 72 ÷ 9 = 8 years. It's a good estimate for everyday rates:

It works for prices too: at 3% inflation, prices roughly double in 24 years.

When compounding works against you

Debt. If unpaid interest is added to what you owe, you pay interest on interest. 1,000 at 2% a month with no payments grows to 1,268.24 in a year, an effective 26.82%, not 24%. Our guide to flat and reducing-balance loans shows how loan rates are quoted.

Inflation. Your real return is roughly (1 + interest rate) ÷ (1 + inflation) − 1. At 5% interest and 3% inflation, that's about 1.94% a year. And 10,000 kept for 10 years at 3% inflation will buy only what about 7,440.94 buys today.

Fees and tax. A small yearly charge compounds as well. 10,000 growing at 7% for 30 years reaches 76,122.55; at 6% it reaches 57,434.91. That one percentage point costs 18,687.64.

How to do it with our tools

The Compound Interest Calculator runs in your browser and shows the balance year by year.

1. Enter your Starting amount and Currency, and a Monthly deposit if you'll add money regularly.
2. Under Deposit at, choose End of each month or Start of each month.
3. Type the Interest rate (% a year) and the number of Years.
4. Pick the Compounding: Monthly, Yearly, Quarterly or Daily.
5. Read the Final balance, You put in and Interest earned, then the Year by year table.

To check it, enter 10,000, no deposit, 6%, 10 years and Yearly: the final balance is 17,908.48, as in the table above. The defaults (10,000 plus 200 a month at 6% for 10 years, compounded monthly) give the 50,969.84 from the deposits example.

The Simple Interest Calculator shows the simple version (10,000 at 5% for 3 years gives 1,500), and the Loan Calculator covers the borrowing side.

The results are estimates. The calculator assumes the same rate every year and no fees, tax or withdrawals. Deposits made part-way through a compounding period grow at an equivalent monthly rate, so an account that credits interest once a year may show a slightly different figure.

Common mistakes

• Comparing headline rates with different compounding. Compare the AER, APY or other effective rate instead.
• Typing 6 instead of 0.06 in the formula. Rates go in as decimals.
• Treating a projection as a promise. Savings rates change and investments can fall.
• Forgetting inflation, fees and tax. They compound too.
• Waiting for a bigger amount to start. Time adds more than frequency does.

This guide is general information, not financial advice. Rates, tax rules and savings products change and differ by country, so check official guidance such as MoneyHelper in the UK or your own country's regulator, or speak to a qualified adviser.

Spotted a mistake or something out of date? Tell us and we'll fix it.