How Compound Interest Works: Formula, Examples and the Rule of 72

What is compound interest?

With compound interest, the interest you earn is added to your balance, and the next round of interest is worked out on the larger balance. Your money grows on top of what has already grown, which is why people describe it as interest on interest.

It applies to savings accounts, fixed deposits and many investments. It also applies to loans and credit cards, where it works in the opposite direction by making what you owe grow.

Compound interest and simple interest

Simple interest is paid only on the original amount. If you put 10,000 into an account at 8 percent simple interest, you earn 800 every year. After 10 years you have earned 8,000 and the total is 18,000.

With compound interest at the same rate, the first year also earns 800, but in the second year interest is paid on 10,800, and so on. After 10 years the total is about 21,589, so you have earned about 11,589 in interest. The extra 3,589 compared with simple interest comes entirely from compounding.

The compound interest formula

The formula is: A = P x (1 + r / n)^(n x t), where A is the final amount. The compound interest earned is A - P.

• P. The principal, which is the amount you start with.
• r. The yearly interest rate as a decimal. 8 percent is 0.08.
• n. How many times a year the interest is compounded. Annually is 1, quarterly is 4 and monthly is 12.
• t. The time in years.

Worked example: 10,000 for 10 years

Say you invest 10,000 at 8 percent a year, compounded once a year, for 10 years. Put the numbers in the formula: A = 10,000 x (1 + 0.08)^10 = 10,000 x 2.158925, which is about 21,589.25.

Your money has more than doubled. The interest earned is 21,589.25 - 10,000 = 11,589.25. You never added a single extra deposit, and the growth came only from time and compounding.

How compounding frequency changes the result

The more often interest is added, the faster the balance grows, because new interest starts earning sooner. Take the same 10,000 at 8 percent for 10 years.

• Compounded annually. The final amount is about 21,589.
• Compounded quarterly. The final amount is about 22,080.
• Compounded monthly. The final amount is about 22,196.

Going from yearly to monthly compounding adds about 600 here. The gain from more frequent compounding is real but smaller than the effect of a higher rate or a longer time. When you compare accounts, look at the annual percentage yield, or APY, which already includes the effect of compounding. For example, 8 percent compounded monthly equals an APY of about 8.30 percent.

The power of regular deposits

Most people do not invest one lump sum. They add money every month. The formula for regular deposits at the end of each month is: future value = deposit x ((1 + i)^n - 1) / i, where i is the monthly rate and n is the number of months.

If you deposit 200 every month at 6 percent a year, compounded monthly, for 20 years, then i = 0.005 and n = 240. The future value is about 92,408. You paid in 200 x 240 = 48,000, so about 44,408 of the final amount is interest. Starting early and staying consistent does most of the work.

The rule of 72

The rule of 72 is a quick way to estimate how long it takes to double your money. Divide 72 by the yearly interest rate. At 8 percent, 72 / 8 = 9 years. At 6 percent, it takes about 12 years, and at 12 percent, about 6 years.

It is only an estimate, but it is close for rates between about 4 and 15 percent. It also shows why a higher rate or a few extra years makes such a big difference.

When compound interest works against you

Compounding does not care whether you are saving or borrowing. On a credit card or a loan with unpaid interest, the interest is added to what you owe and then earns more interest. A balance that is left alone can grow quickly.

The same math that helps a saver hurts a borrower. Paying off high-interest debt early is often one of the best uses of spare money, because you stop interest from growing on interest.

How to make compounding work for you

• Start as early as you can. Time is the biggest factor. Money invested for 30 years grows far more than the same money invested for 10.
• Add money regularly. Monthly deposits, even small ones, build up and then compound too.
• Leave the interest in. Withdrawing interest stops it from earning more interest.
• Compare the APY, not just the rate. Two accounts with the same rate can pay different amounts if they compound at different intervals.
• Watch fees and taxes. Charges and taxes reduce your real growth, so look at what you keep after them.
• Keep inflation in mind. If prices rise by 5 percent a year, an 8 percent return grows your buying power by much less.

Common compound interest mistakes

• Treating projected returns as certain. A savings rate may be fixed, but investment returns go up and down and are not guaranteed.
• Mixing up the rate and the time unit. If you use a yearly rate, time must be in years. For monthly figures, divide the rate by 12 and count months.
• Forgetting fees. A fee of 1 or 2 percent a year takes a large share of your growth over decades.
• Ignoring inflation and tax. The number on the screen is not the same as what you can spend in the future.

Try the calculator

Use our free compound interest calculator to test different amounts, rates and time periods and see how the result changes. It is free and needs no signup. This guide is for general information and is not financial advice, and the results are only estimates. Real returns depend on the product, fees, taxes and the market.

Frequently asked questions