How Compound Interest Works (With Real Examples You Can Check)

Compound interest is the reason a small amount saved early can outgrow a much larger amount saved late, and the reason debt can spiral when it is ignored. The idea is simple: you earn interest not only on the money you put in, but also on the interest you have already earned. This guide explains how it works, shows the arithmetic in full, and points out the mistakes that make people underestimate it.

The idea in one example

Put $1,000 in an account that pays 10 percent a year and leave it alone. After the first year you have $1,100. In the second year, interest is paid on $1,100, not on $1,000, so you earn $110 and finish with $1,210. In the third year you earn $121 and reach $1,331. With simple interest you would only ever earn $100 a year, and after three years you would have $1,300. The extra $31 is the effect of compounding, and it keeps growing.

The formula

For a lump sum, the balance after a number of years is A = P × (1 + r ÷ n)^(n × t). P is the amount you start with, r is the yearly interest rate written as a decimal, n is how many times a year interest is added, and t is the number of years. The part in brackets is the growth factor for one compounding period, and the exponent applies it again and again.

With $10,000 at 6 percent compounded monthly, r ÷ n is 0.005, n × t for 20 years is 240 periods, and the balance is $10,000 × 1.005^240 = $33,102. Nothing was added along the way. The money more than tripled purely because interest kept being added to a growing balance.

Time is the biggest lever

Doubling the rate does not double the result, and doubling the time does much more than that. Take $10,000 compounded monthly at 6 percent:

• After 10 years: $18,194
• After 20 years: $33,102
• After 30 years: $60,226

The second decade added about $14,900, and the third added about $27,100. Each decade adds more than the one before, because the balance it works on is bigger. That is why starting early matters so much, and why the last few years of a long investment produce a surprisingly large share of the final total.

Regular deposits change the picture

Most people do not invest a single lump sum. They add money every month, and each deposit starts its own compounding clock. Deposit $200 a month at 7 percent for 40 years and the balance reaches about $524,963, even though you only paid in $96,000. Deposit the same $200 for 30 years and you reach about $243,994. The extra ten years cost only $24,000 in deposits and produced roughly $281,000 more.

The deposits at the start of the period do most of the work, because they have the longest to grow. That is the reason financial planners keep repeating the same advice: begin now, even with a small amount, and increase it when you can.

Does compounding frequency matter?

A little, but less than people expect. $10,000 at 5 percent for 10 years becomes $16,288.95 when interest is added once a year, $16,470.09 when it is added monthly and $16,486.65 when it is added daily. Moving from yearly to daily adds under $200 over ten years, while moving from 5 to 6 percent adds over $1,700. When comparing accounts, look at the APY (annual percentage yield), which already includes the effect of compounding.

Compounding works against you on debt

The same maths that grows savings makes debt grow. A credit card balance at 24 percent APR compounds monthly at 2 percent, so unpaid debt doubles in about three years. That is why paying off high-interest debt is often the best "investment" available: clearing an 18 percent balance is a guaranteed 18 percent return, which is far more than most savings accounts pay.

Common mistakes

• Comparing nominal rates that compound at different frequencies without looking at the APY.
• Forgetting inflation: a 5 percent return with 3 percent inflation is only about 1.9 percent in real terms.
• Assuming a steady return. Real investments go up and down, so treat any calculation as an illustration.
• Stopping deposits when markets fall, which removes the deposits that would buy at low prices.

Try your own numbers

The Compound Interest Calculator lets you enter a starting amount, a monthly deposit, a rate, a number of years and the compounding frequency, and shows a chart and a year-by-year table. To see what the final amount would really buy, check it with the Inflation Calculator. To plan for a specific target, use the Savings Goal Calculator, and to work out the growth rate of an investment you already have, use the CAGR Calculator. For the difference between compounding and non-compounding interest, read simple vs compound interest.