Compound Interest Formula Explained: Examples and Inflation

Compound interest is interest earned on your original money plus on the interest it has already earned. Because each year’s interest is added to the balance, the growth speeds up over time: $10,000 at 7% a year becomes about $19,700 after 10 years but about $149,700 after 40.

This guide explains the formula, how compounding frequency changes the result, why time is the biggest factor, and how inflation affects what your money can actually buy. It is general information, not financial advice.

Simple vs compound interest

With simple interest, you earn interest only on the original amount. With compound interest, interest is added to the balance and then earns interest itself. The SEC’s investor education site, Investor.gov, uses the same idea in its explanation of compound interest for students.

Take $10,000 at 5% a year:

• Year 1 interest: $10,000 × 0.05 = $500. Balance: $10,500.
• Year 2 interest: $10,500 × 0.05 = $525, not $500, because last year’s interest now earns interest too.

After 10 years, simple interest gives $15,000. Compound interest gives $16,288.95. The gap keeps widening every year.

The compound interest formula

Example: $10,000 at 5%, compounded monthly for 10 years.

The interest earned is A − P = $6,470.09. For quick estimates of how long money takes to double, see our guide to the Rule of 72.

How compounding frequency changes the result

The more often interest is added, the sooner it starts earning interest of its own. Here is $10,000 at a 5% annual rate over 10 years:

Two lessons stand out. First, frequency matters, but not hugely: moving from annual to daily compounding adds about $198 here. Second, the gains shrink as compounding gets more frequent; daily and continuous are almost identical.

When comparing savings accounts or deposits, compare the effective annual rate (in the US, the APY), because it already includes the compounding frequency.

Time is the most powerful factor

The rate and frequency matter, but time matters most, because growth builds on growth. Here is $10,000 at 7% a year, compounded annually:

With simple interest, the balance grows by the same $700 every year. With compound interest, it roughly doubles every 10 years, so the last decade adds more than the first three decades combined.

Starting early: a worked example

Two savers each earn 7% a year, compounded monthly, and both stop at age 65.

• Asha saves $200 a month from 25 to 35, then stops. She puts in $24,000.
• Ben saves $200 a month from 35 to 65. He puts in $72,000.

At 65, Asha has about $280,968 and Ben has about $243,994. Asha contributed a third as much but ends with more, because her money had 30 extra years to compound. Real returns vary from year to year, so treat this as an illustration of the principle, not a forecast. You can model regular savings with the SIP calculator, and our guide on SIP vs lumpsum investing explains what changes when returns are not steady.

Compound interest also works against you

The same maths applies to debt. Credit card balances, payday loans and unpaid loans compound too. A balance you do not pay off is charged interest on last month’s interest. That is why paying down high-rate debt is often the best “return” available: every dollar repaid stops compounding against you.

Inflation: the hidden subtraction

Inflation is the rise in prices over time. If your money grows by 5% a year but prices rise by 3% a year, your purchasing power grows by much less than 5%.

With a 5% return and 3% inflation, the real return is 1.05 ÷ 1.03 − 1 = 1.94% a year.

Over 20 years, $10,000 at 5% becomes $26,533. In today’s money, that is worth only about $14,691. And $10,000 kept as cash earning nothing would buy only about $5,537 worth of today’s goods after 20 years of 3% inflation.

Inflation rates change, and 3% is only an assumption for illustration. The lesson holds at any rate: to grow your real wealth, your money needs to earn more than inflation after tax and fees.

How to make compounding work for you

1. Start early, even with small amounts. Time does the heavy lifting.
2. Reinvest earnings instead of withdrawing interest or dividends.
3. Keep costs low. A 1% annual fee compounds against you just like interest compounds for you.
4. Compare effective rates, not headline rates, when choosing accounts.
5. Clear high-interest debt first, because it compounds faster than most savings grow.

Try different amounts, rates and frequencies in the compound interest calculator. Investor.gov also runs its own compound interest calculator if you want a second check.

FAQ

What is the formula for compound interest?

A = P × (1 + r ÷ n)^{n × t}, where P is the starting amount, r the annual rate as a decimal, n the number of compounding periods per year and t the number of years. Subtract P from A to get the interest earned.

Does daily compounding make a big difference?

Not much compared with monthly. At 5% over 10 years, $10,000 grows to $16,470.09 with monthly compounding and $16,486.65 with daily compounding, a difference of about $17.

How is compound interest different from simple interest?

Simple interest is paid only on the original amount. Compound interest is also paid on interest already earned, so the balance grows faster every year.

What is a real return?

It is your return after inflation, the growth in what your money can actually buy. Calculate it as (1 + nominal return) ÷ (1 + inflation) − 1.