How Compound Interest Works
Compound interest is what happens when the interest your money earns is added to your balance and starts earning interest itself. It is the reason steady saving over many years grows far beyond the sum of your deposits.
Simple vs. compound interest
With simple interest, interest is always calculated on the original amount. Put $10,000 away at 5% and you earn $500 every year: after 20 years you have $20,000.
With compound interest, each year’s interest is calculated on the balance plus everything it has already earned. The same $10,000 at 5% grows to about $26,533 after 20 years. The extra $6,500 comes purely from reinvesting.
| Years | Simple interest | Compound interest |
|---|---|---|
| 5 | $12,500 | $12,763 |
| 10 | $15,000 | $16,289 |
| 20 | $20,000 | $26,533 |
| 30 | $25,000 | $43,219 |
The formula
With no regular deposits, the future value is:
FV = P × (1 + r/n)^(n × t)
where P is the starting balance, r the annual rate, n the number of times interest compounds per year, and t the number of years.
Why time matters most
The table shows a small gap in the early years and a huge one later. Growth is exponential, so the last years contribute far more than the first.
Consider two savers earning 7% a year. One invests $200 a month for 40 years and ends up with about $525,000 after contributing $96,000. The other waits ten years and invests the same $200 for 30 years, ending with about $244,000. Starting a decade earlier more than doubles the result for only $24,000 more in contributions.
The Rule of 72
To estimate how long it takes money to double, divide 72 by the annual return. At 4% it takes about 18 years; at 6%, about 12; at 8%, about 9.
APR vs. APY
Banks quote savings products by APY (annual percentage yield), which already includes the effect of compounding. Loans and credit cards are quoted by APR, which does not. A savings account with a 4.89% nominal rate compounded monthly has an APY of 5.00%.
Where compounding works for you
- High-yield savings accounts and CDs, where interest is added to your balance.
- 401(k) plans and IRAs, where investment gains are reinvested and grow tax-deferred or, in Roth accounts, tax-free.
- Brokerage accounts, when dividends are reinvested.
An employer 401(k) match speeds this up: matched dollars start compounding immediately alongside your own.
Where it works against you
Credit card interest typically compounds daily. Carrying a $5,000 balance at 24% APR and paying only the interest costs around $100 a month without reducing what you owe.
What reduces the real result
- Inflation. If your money earns 5% while prices rise 3%, your real gain is about 2%.
- Fees. A 1% annual fund fee, compounded over decades, takes a meaningful share of the final balance.
- Taxes. Interest in a regular account is taxed each year.
Investment returns are also not fixed or guaranteed: markets have down years.
Results are estimates for informational purposes only and are not financial, tax, legal or medical advice.