Compound Interest Explained: The Formula, Examples and Pitfalls

Compound interest is the process of earning returns not only on the money you put in but also on the returns that money has already earned. Over short periods the effect is modest. Over decades it becomes the single most powerful force in personal finance, working in your favour when you save and against you when you borrow.

Simple interest versus compound interest

With simple interest, you earn a fixed amount based only on your original deposit. Put 10,000 in an account paying 5% simple interest and you earn 500 every year, no matter how long you wait.

With compound interest, the first year's 500 is added to your balance, so in year two you earn 5% on 10,000 plus 500. The extra amount is small at first, but it grows every year because the base keeps getting larger.

The compound interest formula

The standard formula for a single lump sum is:

A = P(1 + r/n)^(nt)

Where:

• A is the final amount
• P is the principal, or starting amount
• r is the annual interest rate as a decimal (5% = 0.05)
• n is the number of times interest compounds per year
• t is the number of years

Adding regular contributions

Most people save regularly rather than investing one lump sum. The future value of a series of equal contributions made at the end of each period is:

FV = PMT × [((1 + r/n)^(nt) − 1) ÷ (r/n)]

Here PMT is the amount you add each period. To find your total, add the lump-sum result and the contributions result together. A compound interest calculator does this instantly, but understanding the formula shows exactly which levers matter: the rate, the time and the amount you contribute.

Worked example: a lump sum

Suppose you invest 10,000 at 6% a year, compounded monthly, for 10 years.

• P = 10,000, r = 0.06, n = 12, t = 10
• A = 10,000 × (1 + 0.06/12)^(120)
• A = 10,000 × (1.005)^120 ≈ 18,194

You would earn roughly 8,194 in interest. With simple interest at the same rate, you would have earned 6,000.

The rule of 72

The rule of 72 is a mental shortcut for estimating how long money takes to double. Divide 72 by the annual rate of return:

• At 4%, money doubles in roughly 18 years.
• At 6%, roughly 12 years.
• At 7%, roughly 10.3 years.
• At 9%, roughly 8 years.

Check it against the formula: 10,000 growing at 7% a year for 10 years becomes about 19,672, very close to double. The rule is an approximation and is most accurate for rates between about 6% and 10%, but it is a handy way to sense-check projections.

Starting at 25 versus 35

The clearest demonstration of compounding is comparing people who start at different ages. Each example below invests 300 a month, earns an assumed 7% average annual return compounded monthly and stops at age 65. Real investment returns vary year to year and are not guaranteed.

Two points stand out. First, starting ten years earlier more than doubles the final balance, even though total contributions are only a third higher. Second, the person who invests for just ten years from age 25 and then stops entirely ends up with more than the person who contributes for thirty years starting at 35. Those early contributions simply had more time to compound.

To reach the same 787,444 by 65 when starting at 35, the late starter would need to invest roughly 645 a month, more than double the early starter's amount.

How compounding frequency affects growth

Interest can compound annually, quarterly, monthly or daily. More frequent compounding produces slightly more growth, because interest starts earning interest sooner. Here is 10,000 at 6% for 10 years:

The difference between monthly and daily compounding is small. The rate itself and the length of time matter far more. When comparing savings accounts, look at the annual percentage yield (APY) or annual equivalent rate (AER), which already include the effect of compounding, so different accounts can be compared fairly. Terminology varies by country.

How inflation and fees erode compounding

Inflation

Inflation reduces what your money can buy. If your savings earn 4% while prices rise 3%, your real return is roughly 1%. At 3% inflation, prices roughly double in 24 years, using the same rule of 72. That is why long-term projections are often shown in today's money, using a real return that subtracts expected inflation. Cash that earns less than inflation loses purchasing power, even though the balance grows.

Fees

Investment fees compound in the opposite direction. A 1% annual fee does not just take 1% once; it reduces the base that future growth builds on, every year. Over 30 years, a fee difference of under one percentage point can reduce a final balance by a substantial amount, often tens of thousands on a modest monthly contribution. Choosing low-cost funds is one of the few investment factors fully within your control.

When compound interest works against you

The same mathematics applies to debt. Credit cards in many countries typically charge annual rates of roughly 18% to 30%, with interest calculated daily or monthly on the outstanding balance.

Worked example: credit card minimum payments

Take a 5,000 credit card balance at 20% APR. Assume the minimum payment is the month's interest plus 1% of the balance, with a floor of 25.

Paying only the minimum more than doubles the cost of the original balance. Minimum payment rules differ between lenders and countries, but the pattern is consistent: the longer a high-rate balance lingers, the more compounding works against you. Paying down expensive debt is effectively a guaranteed return equal to its interest rate.

Common mistakes to avoid

• Waiting to start investing until you can afford a large amount.
• Withdrawing gains early and interrupting compounding.
• Comparing nominal returns while ignoring inflation and fees.
• Treating projected returns as guaranteed.
• Investing while carrying high-interest debt that compounds faster than your investments are likely to grow.

Watch: a visual explainer

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Video by Khan Academy, embedded via YouTube. Private.Finance is not affiliated with the creator.

Frequently asked questions