How Compound Interest Works: A Simple Explanation
Compound interest is often called the most powerful force in personal finance. It is the reason savings started early can grow far larger than savings started late, and also the reason unpaid credit card debt can spiral. This guide explains how compound interest works, with simple numbers, so you can use it to your advantage. To run your own numbers, use our compound interest calculator.
Simple interest vs. compound interest
With simple interest you earn interest only on the money you put in. $1,000 at 5% simple interest earns $50 every year: after 3 years you have $1,150.
With compound interest the interest is added to your balance and the next year’s interest is calculated on the larger amount:
| Year | Start balance | Interest at 5% | End balance |
|---|---|---|---|
| 1 | $1,000.00 | $50.00 | $1,050.00 |
| 2 | $1,050.00 | $52.50 | $1,102.50 |
| 3 | $1,102.50 | $55.13 | $1,157.63 |
The difference looks tiny after three years, just $7.63. But because each year builds on the previous one, the gap grows faster and faster.
The formula
A = P × (1 + r ÷ n)n × t
- A – the final amount
- P – the principal, the amount you start with
- r – the annual interest rate as a decimal (5% = 0.05)
- n – how many times per year interest is added (12 for monthly)
- t – the number of years
Time does the heavy lifting
$10,000 growing at 7% a year becomes about $76,100 after 30 years and about $149,700 after 40 years. The final ten years add more than $73,000, more than the first thirty years combined. Nothing about the investment changed; it simply had more time to compound.
Regular contributions work the same way. Saving $200 a month for 30 years at 6% (compounded monthly) puts in $72,000 of your own money but ends with about $200,900. Almost two thirds of the result is growth. You can model this with the retirement savings calculator.
The rule of 72
To estimate how long it takes money to double, divide 72 by the annual rate:
| Annual rate | Years to double (approx.) |
|---|---|
| 3% | 24 |
| 6% | 12 |
| 8% | 9 |
| 12% | 6 |
The rule works in reverse too: inflation of 3% halves the purchasing power of cash in about 24 years.
How often interest compounds
Banks may add interest yearly, quarterly, monthly or daily. More frequent compounding gives slightly more, because interest starts earning interest sooner. This is why accounts quote an APY (annual percentage yield), which includes compounding, alongside the nominal rate. 5% compounded monthly is an APY of about 5.12%. When comparing savings accounts, compare the APY.
When compound interest works against you
Debt compounds too. A credit card balance at 24% a year roughly doubles in three years if you only make tiny payments, because unpaid interest is added to the balance. That is why paying off high-interest debt is usually the best guaranteed return available. Loans with fixed payments are a different case; see our guide on how loan payments work.
How to make compound interest work for you
- Start as early as possible, even with small amounts.
- Contribute regularly, ideally automatically on payday.
- Reinvest the returns instead of withdrawing them.
- Keep costs low. A 1% yearly fee can eat a large share of long-term growth.
- Be patient. The biggest gains arrive at the end, so avoid interrupting the process.
Key takeaways
- Compound interest is interest earned on interest.
- The longer the time and the higher the rate, the bigger the effect, and time is the factor you control most.
- Divide 72 by the rate to estimate the doubling time.
- The same maths makes debt grow, so clear expensive debt first.
Run your own scenarios with the compound interest calculator or explore all our free tools. This guide is educational and is not financial advice.