Key takeaways
- Compound interest is interest paid on the principal and on interest already earned, so growth builds on itself.
- The standard formula is A = P(1 + r/n)^(nt), where n is the number of compounding periods per year.
- The rule of 72 estimates doubling time: 72 divided by the percentage rate, accurate near typical rates and less so at high ones.
- Time has a large effect: in the example here, 30 years of $100 monthly contributions at 6% end with more than twice the balance of 20 years.
- Compounding also works against you on debt, and investments such as stocks do not earn a fixed rate.
Investor.gov opens its page on small savings with a question: how much does a daily $1 candy bar cost? Its answer is $465.84 or more. Saving one year's $365 instead and investing it at 5% a year, it calculates, would grow to $465.84 after five years and $1,577.50 after 30. The gap between those figures and the simple sum of $365 is compounding: earning a return on the money you put in and on the returns it has already earned.
Simple versus compound growth
Investor.gov's glossary defines compound interest as interest paid on principal and on accumulated interest. Simple interest is paid on the principal only. Here is $1,000 at 6% a year under each:
| Years | Simple interest | Compound interest, yearly | Difference |
|---|---|---|---|
| 10 | $1,600.00 | $1,790.85 | $190.85 |
| 20 | $2,200.00 | $3,207.14 | $1,007.14 |
| 30 | $2,800.00 | $5,743.49 | $2,943.49 |
Simple interest adds the same $60 every year. Compound interest adds 6% of a balance that keeps growing, so the gap widens with time: the difference after 30 years is about fifteen times the difference after 10.
The formula
The standard formula, as set out in Wikipedia's article on compound interest, is:
A = P(1 + r/n)^(nt)
- P: the starting principal
- r: the nominal annual interest rate, as a decimal (6% = 0.06)
- n: the compounding frequency, the number of times per year interest is added
- t: the number of years
- A: the final amount
Worked example: $1,000 at 6% compounded yearly for 20 years gives A = 1,000 × 1.06²⁰ ≈ $3,207.14.
How often interest compounds
Compounding more often helps, but only a little. For a 6% nominal rate, the effective annual rate, the rate that compares products on an equal footing, works out as:
| Compounding | Calculation | Effective annual rate |
|---|---|---|
| Yearly | 1.06 − 1 | 6.000% |
| Monthly | (1 + 0.06/12)¹² − 1 | 6.168% |
| Daily | (1 + 0.06/365)³⁶⁵ − 1 | 6.183% |
Wikipedia notes that many countries require financial institutions to disclose rates on a comparable annual basis, under names such as annual equivalent rate or annual percentage yield. The rate itself and the time invested matter far more than the frequency.
The rule of 72
To estimate how long money takes to double, divide 72 by the annual percentage rate. Wikipedia explains that 72 is used because it has many small divisors and gives a good approximation for typical rates of about 6% to 10%, becoming less accurate at higher rates.
| Rate | Rule of 72 estimate | Exact doubling time |
|---|---|---|
| 2% | 36 years | 35.0 years |
| 6% | 12 years | 11.9 years |
| 8% | 9 years | 9.0 years |
| 12% | 6 years | 6.1 years |
| 24% | 3 years | 3.2 years |
Wikipedia notes the same idea applies to inflation: dividing by the inflation rate estimates how long money takes to lose half its buying power. At 3% inflation, that is roughly 72 ÷ 3 = 24 years.
Regular contributions and starting early
Investor.gov's compound interest calculator asks for an initial amount, a monthly contribution, the number of years, an estimated annual rate, a range of rates to compare and the compounding frequency. Regular contributions give compounding more money to work on. With $100 a month at 6% compounded monthly:
| Saving period | Total contributed | Approximate balance |
|---|---|---|
| 20 years | $24,000 | $46,204 |
| 30 years | $36,000 | $100,452 |
Ten extra years of $100 contributions, $12,000 in all, more than doubles the final balance, because the earlier money has longer to compound. Investing a fixed amount on a schedule is also the idea behind dollar-cost averaging.
When compounding works against you
Debt compounds too. A $1,000 credit card balance at 24% a year, charged as 2% a month with no payments, grows to about $1,268 in a year. Investor.gov's building-wealth guidance notes that interest on consumer debt such as credit cards will likely far outweigh the return you can earn on most investments.
Investments are not fixed-rate accounts. The tables above assume a constant rate. Stocks do not deliver one: Investor.gov notes that large-company stocks as a group have lost money on average about one out of every three years. Stocks versus bonds and risk tolerance cover what that variability means.
Too-good-to-be-true compounding. Run a promised 1% a day through the formula and money doubles in about 70 days (ln 2 ÷ ln 1.01 ≈ 69.7). Promises like that are worth checking against investment fraud red flags.
Learn to Trade Stocks Beginner, one of our education apps, uses a virtual balance, so you can watch positions rise and fall without real money at stake. The investing basics hub lists related guides, including dividend yield.
Good to know
Frequently asked questions
What is compound interest in simple terms?
What is the compound interest formula?
What is the rule of 72?
Do stocks compound like a savings account?
Sources
- Small Savings Add Up to Big Money (opens in a new tab)Investor.gov, U.S. Securities and Exchange Commission — accessed
- Compound Interest Calculator (opens in a new tab)Investor.gov, U.S. Securities and Exchange Commission — accessed
- What is Risk? (opens in a new tab)Investor.gov, U.S. Securities and Exchange Commission — accessed
- Compound interest (opens in a new tab)Wikipedia — accessed
- Rule of 72 (opens in a new tab)Wikipedia — accessed
- Ten Building Blocks for Building Wealth (opens in a new tab)Investor.gov, U.S. Securities and Exchange Commission — accessed
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