What Is Compound Interest?
Compound interest means you earn interest not just on your original principal, but also on the interest you've already accumulated. Each period, your balance grows — and the next period's interest is calculated on that larger number. Over time, this creates an exponential curve rather than a straight line.
The formula is: A = P × (1 + r/n)^(n × t), where P is the principal, r is the annual rate, n is the number of compounding periods per year, and t is years. With regular contributions, each deposit also begins compounding from the moment it's added.
Example Growth: $10,000 at 4%, 5%, and 6%
These tables assume annual compounding on a $10,000 deposit with no additional contributions, so you can isolate the effect of rate and time. Use the calculator above for monthly or daily compounding and added contributions.
| Years | 4% | 5% | 6% |
|---|---|---|---|
| 1 year | $10,400 | $10,500 | $10,600 |
| 5 years | $12,167 | $12,763 | $13,382 |
| 10 years | $14,802 | $16,289 | $17,908 |
| 20 years | $21,911 | $26,533 | $32,071 |
| 30 years | $32,434 | $43,219 | $57,435 |
At 6% over 30 years, $10,000 grows to roughly 5.7× the original amount. A two-percentage-point rate difference (4% vs. 6%) almost doubles the ending balance over the same horizon — which is why expected return is the single most important assumption in any compound-growth projection.
Simple Interest vs. Compound Interest
Simple interest is calculated only on the original principal: A = P × (1 + r × t). Compound interest is calculated on the principal plus all previously earned interest. Over short horizons the two are close. Over longer horizons compound interest pulls dramatically ahead.
| Years at 6% | Simple Interest | Compound Interest (annual) | Difference |
|---|---|---|---|
| 5 years | $13,000 | $13,382 | $382 |
| 10 years | $16,000 | $17,908 | $1,908 |
| 20 years | $22,000 | $32,071 | $10,071 |
| 30 years | $28,000 | $57,435 | $29,435 |
Simple interest is rare in modern finance — most savings accounts, CDs, and loans use some form of compounding. It still appears in some bonds, certain auto loans, and short-term promissory notes, so it's worth recognizing. For practical planning, almost any account you'll encounter compounds at least monthly.
How Compounding Frequency Affects Growth
More frequent compounding means slightly higher returns, because interest is applied to a growing balance more often. Here's an example with $10,000 at 7% for 20 years:
| Frequency | Final Balance |
|---|---|
| Annually | $38,697 |
| Quarterly | $40,064 |
| Monthly | $40,387 |
| Daily | $40,547 |
The difference between annual and daily compounding is about $1,850 on $10,000 over 20 years — noticeable but modest compared to the impact of the rate and time horizon. What matters far more is getting the rate and the time right.
How the Curve Bends Up
Each month, interest is calculated on the prior balance — including earlier interest. That makes the projected balance curve upward rather than increase in a straight line. At 7% annual returns, a one-time $10,000 deposit doubles to roughly $20,000 in about 10 years, then doubles again to $40,000 in the next 10. Each doubling takes the same number of years, so the curve gets steeper as the balance grows.
Two equal contributions made years apart compound to different ending balances because the earlier one accrues interest over more periods. Assuming 7% returns, $5,000 added in year one finishes at about $10,000 after 10 years and $20,000 after 20; the same $5,000 added in year 11 only reaches about $10,000 by year 20. To work the same question backward — "how much do I need to save each month to hit a target by a specific date?" — use the savings goal calculator.
APY vs. APR
APR (Annual Percentage Rate) is the stated rate. APY (Annual Percentage Yield) is the effective rate after accounting for compounding — it's always equal to or higher than APR. The formula is: APY = (1 + r/n)^n − 1. Banks advertise APY on savings accounts and APR on loans — intentionally, since APY sounds better for savings and APR sounds lower for debt. Use the APY calculator to convert between any nominal rate and APY at any compounding frequency.
Frequently Asked Questions
What rate should I use for investment projections?
The S&P 500 has returned roughly 10% nominally and 7% after inflation on average over long periods. Financial planners commonly use 6–8% for long-term projections, which accounts for a diversified portfolio and inflation. For savings accounts and CDs, use the actual rate your bank offers. For a "real" return (after inflation), subtract roughly 3% from any nominal rate.
Does compound interest work the same way for debt?
Yes — and against you. Credit card interest compounds daily or monthly on your unpaid balance, which is why carrying a balance is so damaging. A $5,000 balance at 22% APR compounds to nearly $44,000 in 10 years if you make no payments. The same math that builds wealth in investments destroys it in high-interest debt.
What's the Rule of 72?
Divide 72 by your annual interest rate to estimate how many years it takes to double your money. At 6%, your money doubles in about 12 years. At 9%, about 8 years. At 1% (a typical savings account), it takes 72 years. It's a quick mental check for whether a rate is worth getting excited about.