How Compound Interest Works, With Examples and Charts

Albert Einstein is often quoted as calling compound interest the eighth wonder of the world, though there is no good evidence that he said it. You do not need the quote to see why the idea matters. Compounding is the reason a modest monthly saving habit can grow into a large sum, and the reason a credit card balance can grow faster than you expect.

Simple interest against compound interest

With simple interest the interest is always worked out on the original amount. If you put in $10,000 at 7%, you earn $700 every year, no matter how long it stays there. After 30 years you would have $10,000 + 30 × $700 = $31,000.

With compound interest each year's interest is added to the balance, so next year's interest is calculated on a bigger number. The same $10,000 at 7%, compounded monthly, becomes $81,165 after 30 years, more than two and a half times the simple-interest result.

The formula

1. Take $10,000 at 7% (r = 0.07), compounded monthly (n = 12), for 30 years (t = 30).
2. Work out the rate per period: 0.07 / 12 = 0.005833.
3. Work out the number of periods: 12 × 30 = 360.
4. Raise (1.005833) to the power 360, which is about 8.116, then multiply by $10,000 to get $81,165.

You can check this with our Compound Interest Calculator.

Adding money every month

Most people do not invest a single lump sum. They add money regularly, and each deposit then starts compounding from the day it goes in. Suppose you save $200 a month at an average return of 7% a year. After 30 years you will have put in $72,000 and the account will hold about $243,994.

View the numbers behind the monthly-plan chart

Year	Your deposits	Growth	Balance
1	$2,400	$79	$2,479
5	$12,000	$2,319	$14,319
10	$24,000	$10,617	$34,617
15	$36,000	$27,392	$63,392
20	$48,000	$56,185	$104,185
25	$60,000	$102,014	$162,014
30	$72,000	$171,994	$243,994

Notice when growth overtakes deposits. In this example the account earns more than you contribute after roughly 19 years, and from then on most of the balance is growth.

The effect of the return you earn

Small differences in the rate become large differences over decades. The next chart repeats the $200 monthly plan at three average returns.

These are steady average returns used for teaching. Real investments rise and fall, and the order of the good and bad years affects the outcome. Treat the numbers as an illustration of the maths, not as a forecast.

How much does compounding frequency matter?

Banks quote an interest rate and then say how often it is added: daily, monthly, quarterly or yearly. More frequent compounding gives a little more, but the gain is small compared with the effect of time.

Start early, even with less

Because growth builds on itself, the first dollars you invest do the most work. Compare two people who both earn 7% on the same schedule:

• Early saver: puts in $200 a month for the first 10 years (say ages 25 to 35), then stops and leaves the money alone for 30 more years.
• Late saver: waits 10 years, then puts in $200 a month for 30 years (ages 35 to 65).

This does not mean you should stop saving after 10 years, because someone who starts early and keeps going does better still. It shows how powerful the early years are. If you have started late, saving more each month helps close the gap.

The rule of 72

A quick way to estimate how long money takes to double is to divide 72 by the annual return in percent. At 6% the money doubles in about 12 years, and at 9% in about 8 years.

View the rule of 72 against the exact answer

Annual return	Rule of 72 estimate	Exact years to double
2%	36.0 years	35.0 years
4%	18.0 years	17.7 years
6%	12.0 years	11.9 years
8%	9.0 years	9.0 years
10%	7.2 years	7.3 years
12%	6.0 years	6.1 years

The shortcut is closest for returns between about 6% and 10% and drifts for very low or very high rates.

When compounding works against you

The same maths applies to debt. A credit card charging 24% a year, compounded monthly, adds about 2% to the balance each month. If you only pay the minimum, the interest keeps being added to a balance that shrinks slowly. Paying off high-interest debt is equivalent to earning a guaranteed return equal to that interest rate, which is hard to match elsewhere.

Practical steps

• Start now with whatever amount you can, and raise it when your income rises.
• Automate deposits so that saving happens before you can spend the money.
• Keep fees low, because a fee of 1% a year takes a visible slice of the growth over 30 years.
• Leave the money invested rather than withdrawing early, since withdrawals also lose the future compounding on them.
• Clear expensive debt first, especially cards, before investing for modest returns.

Common questions

Sources and further reading

• Investor.gov (U.S. SEC): Compound interest calculator
• Consumer Financial Protection Bureau: Consumer tools

This guide is for general education and is not investment advice. The returns used in the examples are steady averages chosen to illustrate the maths. Real investments change in value and can lose money.