Compound interest: how growth on growth builds wealth

Compound interest is what happens when your returns start earning returns of their own. Put $10,000 somewhere that pays 7% a year and leave the earnings in place. In year one you earn $700. In year two you earn 7% on $10,700, which is $749. The extra $49 is interest on interest, and that small gap widens every year until it dominates the result.

Compounding is not a product or a strategy. It is arithmetic, and it applies to anything that grows by a percentage: savings accounts, bonds, reinvested dividends, a business's earnings, and debts too. This guide shows the formula, the rule of 72 shortcut, worked tables for a lump sum and for monthly saving, and the forces that quietly work against compounding: fees, taxes, inflation and losses.

Simple interest versus compound interest

Simple interest is paid only on the original amount. $10,000 at 7% simple interest earns $700 every year, forever. After 30 years you have $10,000 + 30 × $700 = $31,000.

Compound interest is paid on the original amount plus everything it has already earned. The same $10,000 at 7% compounded once a year becomes about $76,123 after 30 years, roughly two and a half times the simple-interest result.

For the first few years the two lines are almost on top of each other. The difference grows slowly and then very quickly, because each year's interest is calculated on a larger base. That shape, flat at first and steep later, is the signature of anything that compounds. It also explains why compounding feels unimpressive to beginners: most of the reward arrives in the final third of the period.

The compound interest formula

With annual compounding (m = 1) this simplifies to P × (1 + r)ᵗ. Each year the balance is multiplied by the same growth factor. Multiplying repeatedly by 1.07 is what makes the curve bend upward.

How often interest compounds

Banks quote an annual percentage rate (APR) and often compound monthly or daily. More frequent compounding adds a little extra, which shows up in the annual percentage yield (APY), the rate you actually earn over a year.

The jump from yearly to monthly compounding is modest. The jump from monthly to daily is smaller still. Frequency matters far less than the rate itself and the number of years.

The rule of 72

You can estimate how long money takes to double without a calculator: divide 72 by the annual percentage rate.

The rule is most accurate between roughly 6% and 10%. It works in reverse too: to double money in 6 years you need about 72 ÷ 6 = 12% a year. And it works for anything that compounds, including prices. At 3% inflation, the cost of living doubles in about 24 years, which means the purchasing power of cash held under a mattress halves over that period.

Adding money every month

Most people don't invest one lump sum. They add a little at a time. Regular contributions compound as well, and the formula for a stream of equal deposits is:

The second half of that example is the real lesson. The final decade of a 30-year plan produces more growth than the first two decades combined, and only money that is already invested gets to take part in it.

Compounding in the stock market

Stocks don't pay a fixed rate, but the same arithmetic applies to their returns. A company that retains its profits and reinvests them at a good rate grows its earnings on a growing base. A shareholder who reinvests dividends buys more shares, which then pay their own dividends.

The difference from a bank account is that stock returns vary from year to year, and some years are negative. Long-run averages are therefore expressed as a compound annual growth rate (CAGR), the steady rate that would turn the starting value into the ending value:

The SPDR S&P 500 ETF (SPY) closed its first month in February 1993 at about $44 and closed October 29, 2026 at about $769 in Finabase's data. That works out to a price-only CAGR of roughly 8.8% a year over 33.7 years, as the What is a stock? A complete beginner’s guide to shares guide shows. Reinvested dividends would raise it further.

Losses compound too

Compounding is symmetrical. Percentage losses are applied to a shrinking balance, and the gain needed to recover is always larger than the loss.

That is why an investment that rises 50% one year and falls 50% the next is down 25%, not flat: $100 becomes $150, then $75. Avoiding large losses does as much for long-run compounding as chasing large gains.

What works against compounding

Fees. An annual fee is a negative return that compounds every year. Over long periods the effect is large.

Taxes. Interest, dividends and realized gains taxed every year reduce the amount left to compound. In the US, tax-advantaged accounts such as 401(k)s and IRAs let returns compound without annual tax, subject to IRS contribution limits and withdrawal rules.

Inflation. A 7% return with 3% inflation is roughly a 4% gain in purchasing power. The "real" compounding rate is what matters for what your money will buy.

Interruptions. Withdrawing money, selling in a panic and sitting in cash, or stopping contributions all reset part of the compounding clock.

Debt. Credit card balances compound against you, often at rates far above what any investment reliably earns. Paying down high-rate debt is itself a high, guaranteed return.

Common mistakes with compounding

• Using the average return instead of the compound return. Returns of +50% and −50% average 0% but compound to −25%. Volatility lowers the compound rate below the simple average.
• Projecting a straight line from a great stretch. A rate that held for 10 years may not hold for the next 30. Treat any long-run projection as a range, not a promise.
• Ignoring the base. A 20% gain on $1,000 is less money than 5% on $10,000. Rates and amounts both matter.
• Forgetting the end of the curve. Because so much of the growth arrives late, cashing out a few years early gives up a disproportionate share of the final result.

Compounding compared with other growth patterns

How Finabase helps

Finabase is a research app, not a bank or a broker, so it doesn't hold or grow your money. It does give you the data to see compounding at work. The comparison page keeps sets of symbols and shows their period returns and a chart rebased to the same starting point, which makes the difference between, say, a stock index fund and a bond fund visible over years. The Treasury page shows current US government yields, a useful reference for what "low-risk" money compounds at today. And each symbol's dividends tab lists the payouts that reinvestment would have compounded.

Frequently asked questions

How much will $10,000 be worth in 20 years?

It depends entirely on the rate. At 4% a year it becomes about $21,900, at 7% about $38,700, and at 10% about $67,300, before taxes, fees and inflation. Use the formula P × (1 + r)ᵗ with your own assumption, and test a few rates to see the range.

Is the rule of 72 accurate?

It is a close approximation for rates between about 6% and 10%, usually within a few months of the exact answer. At very low or very high rates it drifts: at 24% it says three years when the exact figure is about 3.2.

Does compound interest work in the stock market?

Yes, through reinvested dividends and retained company earnings, but not at a fixed rate. Stock returns vary each year, so the long-run result is described with a compound annual growth rate, and losses compound as well as gains.

What is the difference between APR and APY?

APR is the stated annual rate before compounding within the year. APY includes the effect of compounding. A 6% APR compounded monthly is an APY of about 6.17%.

Summary

Compound interest is growth on growth: each period's return is earned on a balance that already includes past returns. The formula P × (1 + r)ᵗ puts time in the exponent, so the years you stay invested matter as much as the rate you earn, and the rule of 72 turns any rate into a quick doubling time. The same arithmetic punishes fees, taxes, inflation and large losses, which compound against you. Understanding the curve, slow at first and steep later, is the reason patient, low-cost, consistent investing tends to do so much of the work.