What Is Compound Interest? Formula, Examples and Tables
What is compound interest? Learn the formula, see a worked example with year-by-year tables, compare simple vs compound interest, and use the Rule of 72.
This guide is general information only, not professional financial, legal or technical advice. Menus and rules can vary by device and country.
Compound interest is interest earned on both your original money and on the interest it has already earned. Because each period's interest is added to the balance, the next period's interest is calculated on a bigger number, so your money grows faster and faster over time.
The same effect works against you when you borrow. Unpaid interest on debt can be added to what you owe, so balances can snowball.
Quick answer
- Compound interest = interest on your principal plus past interest.
- Formula: A = P × (1 + r/n)^(n × t).
- 1,000 at 5% a year, compounded yearly, grows to about 1,628.89 in 10 years.
- Time matters most: starting earlier usually beats saving more later.
- The Rule of 72: divide 72 by the yearly rate to estimate how many years it takes to double.
- On debt, compounding makes balances grow, so pay high-interest debt quickly.
This is general information, not personal financial advice. All rates below are examples, not predictions or promised returns.
How compound interest works
Three things decide how much compound interest you earn:
- Principal: the amount you start with.
- Interest rate: the yearly percentage you earn (or pay).
- Compounding frequency: how often interest is calculated and added, such as yearly, monthly or daily.
Time is the fourth ingredient. The longer interest keeps compounding, the bigger the effect.
Here's the idea with 1,000 at 5% a year:
- Year 1: 5% of 1,000 = 50. New balance: 1,050.
- Year 2: 5% of 1,050 = 52.50. New balance: 1,102.50.
Year 2 earns 2.50 more than year 1 because the first year's 50 of interest is now earning interest too.
The compound interest formula
The standard formula is:
A = P × (1 + r/n)^(n × t)
- A = final amount
- P = principal (starting amount)
- r = yearly interest rate as a decimal (5% = 0.05)
- n = number of times interest compounds per year (yearly = 1, monthly = 12, daily = 365)
- t = number of years
To find just the interest earned, subtract the principal: Interest = A − P.
Worked example: step by step
Let's calculate 1,000 at 5% compounded yearly for 10 years.
- Convert the rate to a decimal: 5% = 0.05.
- Divide by compounding periods: 0.05 ÷ 1 = 0.05.
- Add 1: 1 + 0.05 = 1.05.
- Work out the exponent: n × t = 1 × 10 = 10.
- Raise to the power: 1.05^10 ≈ 1.628895.
- Multiply by the principal: 1,000 × 1.628895 ≈ 1,628.89.
So you would earn about 628.89 in interest without adding any more money.
Simple vs compound interest: year-by-year table
Simple interest is paid only on the original principal. Compound interest is paid on the growing balance. Here is 1,000 at 5% a year, compounded yearly:
| Year | Simple interest balance | Compound interest balance | Difference |
|---|---|---|---|
| 1 | 1,050.00 | 1,050.00 | 0.00 |
| 2 | 1,100.00 | 1,102.50 | 2.50 |
| 3 | 1,150.00 | 1,157.63 | 7.63 |
| 5 | 1,250.00 | 1,276.28 | 26.28 |
| 10 | 1,500.00 | 1,628.89 | 128.89 |
| 20 | 2,000.00 | 2,653.30 | 653.30 |
| 30 | 2,500.00 | 4,321.94 | 1,821.94 |
At first, the difference is tiny. After 30 years, compounding produces almost 1,822 more than simple interest from the same starting amount and rate.
Does compounding frequency matter?
More frequent compounding gives a slightly higher result, because interest starts earning interest sooner. Here is 1,000 at 5% for 10 years:
| Compounding | Periods per year (n) | Balance after 10 years |
|---|---|---|
| Yearly | 1 | 1,628.89 |
| Quarterly | 4 | 1,643.62 |
| Monthly | 12 | 1,647.01 |
| Daily | 365 | 1,648.66 |
The difference is real but small. The interest rate, how much you add, and how long you leave the money matter far more than daily vs monthly compounding.
Adding money regularly
Most people don't invest one lump sum and walk away. They add a bit each month. The formula for regular monthly deposits with monthly compounding is:
FV = PMT × [((1 + i)^N − 1) ÷ i]
where PMT is the monthly deposit, i is the monthly rate (yearly rate ÷ 12) and N is the number of months.
Example: 100 a month at 5% a year, compounded monthly:
| Years saving | Total you put in | Estimated balance |
|---|---|---|
| 30 years (360 months) | 36,000 | 83,225.86 |
| 40 years (480 months) | 48,000 | 152,602.02 |
Saving for 10 more years adds 12,000 of deposits but nearly 69,400 to the final balance. That is why starting early is so powerful. Real investments don't earn a steady rate, so treat these as illustrations only. Our guide to investing for beginners explains the risks.
The Rule of 72: a quick shortcut
To estimate how long money takes to double, divide 72 by the yearly interest rate.
| Yearly rate | Rule of 72 estimate | Exact years to double (yearly compounding) |
|---|---|---|
| 2% | 36 years | 35.0 |
| 4% | 18 years | 17.7 |
| 6% | 12 years | 11.9 |
| 8% | 9 years | 9.0 |
| 10% | 7.2 years | 7.3 |
It is an estimate, but it is close for typical rates and easy to do in your head.
When compound interest works against you
Compounding helps savers but hurts borrowers. Credit cards can charge yearly rates of 18% or more. If 1,000 of card debt sat untouched at 20% a year, compounded monthly, it would grow to about 1,219.39 after one year (actual card calculations, fees and minimum payments vary).
That's why paying off high-interest debt is often one of the best "returns" you can get. See how to get out of debt for payoff strategies.
How to make compound interest work for you
- Start as early as you can. Time is the biggest driver of growth.
- Add money regularly. Automatic monthly deposits keep the snowball rolling. Our tips on how to save money can help free up cash.
- Reinvest your interest. Leave earnings in the account so they compound.
- Compare rates and fees. A slightly higher rate or lower fee makes a big difference over decades.
- Avoid withdrawals. Taking money out resets part of the compounding.
- Pay off high-interest debt. Stop compounding from working against you.
Common mistakes
- Confusing the rate per year with the rate per period. Always divide the yearly rate by n.
- Forgetting inflation. Rising prices reduce what your future balance can buy.
- Ignoring fees. Yearly fees reduce the amount that compounds.
- Believing "guaranteed high returns." Promises of big, risk-free compounding are a common scam tactic.
- Waiting for the "perfect" time to start. Delay costs more than a small starting amount.
Frequently Asked Questions
What is compound interest in simple words?
It is "interest on interest." You earn interest on your starting money, and then that interest also earns interest. Over time, the growth speeds up like a snowball rolling downhill.
What is the formula for compound interest?
The formula is A = P × (1 + r/n)^(n × t), where P is the starting amount, r is the yearly rate as a decimal, n is how many times per year interest is added, and t is the number of years. Subtract P from A to see the interest earned.
What is the difference between simple and compound interest?
Simple interest is calculated only on the original amount. Compound interest is calculated on the original amount plus all interest added so far. Over long periods, compound interest produces much larger totals.
How often is interest compounded?
It depends on the account or loan. Common options are yearly, quarterly, monthly and daily. More frequent compounding gives slightly more growth, but the rate and time invested matter much more.
Is there a free compound interest calculator?
Yes. The US Securities and Exchange Commission's Investor.gov site offers a free compound interest calculator. You can enter a starting amount, monthly contribution, number of years, estimated rate and compounding frequency.