Finance guide
How to Calculate Compound Interest (and How It Differs From Simple Interest)
The compound interest formula with a worked example, how compounding frequency and monthly deposits change the result, and the rule of 72.
By M2Toolkit Editorial TeamPublished 7 min read
Quick answer
P is the starting amount, r the annual rate as a decimal, n how many times interest compounds per year and t the number of years. $10,000 at 5% compounded yearly for 10 years grows to $16,288.95. With simple interest it would be $15,000.
The difference between simple and compound interest is small at first and enormous later. Simple interest is paid only on your original money; compound interest is paid on your money plus the interest it has already earned.
Simple interest
$10,000 at 5% for 10 years earns $500 a year, $5,000 in total. Simple interest is used for some short-term loans, bonds' coupon payments and many classroom problems.
Try the free Simple Interest CalculatorInterest on a fixed amount, in years, months or days.Compound interest, year by year
| Year | Simple interest balance | Compound (yearly) balance |
|---|---|---|
| 1 | $10,500 | $10,500.00 |
| 5 | $12,500 | $12,762.82 |
| 10 | $15,000 | $16,288.95 |
| 20 | $20,000 | $26,532.98 |
| 30 | $25,000 | $43,219.42 |
After 30 years, compounding has earned $33,219 of interest versus $15,000 — more than double — from the same rate.
Does compounding frequency matter?
Less than you might think. At 5% for 10 years on $10,000:
| Compounding | Balance after 10 years | Effective annual rate |
|---|---|---|
| Yearly | $16,288.95 | 5.00% |
| Monthly | $16,470.09 | 5.12% |
| Daily | $16,486.65 | 5.13% |
The rate and the time invested matter far more than how often interest is added.
Adding regular deposits
Most people save monthly rather than investing one lump sum. $10,000 plus $200 a month at 7% compounded monthly grows to about $144,573 in 20 years — of which $58,000 is your own money and the rest is growth.
Try the free Compound Interest CalculatorStarting amount, monthly deposits and any compounding frequency, with a yearly table.The rule of 72
To estimate how long money takes to double, divide 72 by the annual rate: at 6%, about 12 years; at 9%, about 8 years. It's a quick mental check that works well for rates between about 4% and 12%.
Frequently asked questions
What's the difference between APR and APY?
APR is the stated annual rate. APY (or AER) includes the effect of compounding, so it shows what you actually earn in a year. A 5% APR compounded monthly is a 5.12% APY.
Do investments really compound?
Reinvested dividends and growth compound in a similar way, but returns vary year to year. Calculators assume a steady average rate, which is a simplification.