How does compound interest work?
Last updated March 26, 2026
Compound interest earns interest on your interest. With $10,000 at 7% compounded annually, you’ll have $19,672 after 10 years — nearly double — without adding a penny. Add $200/month and you’ll have $54,714 with monthly compounding.
How to Calculate
- 1
Start with your principal (initial investment)
- 2
Determine the annual interest rate and compounding frequency
- 3
Apply the formula: A = P(1 + r/n)^(nt)
- 4
For regular contributions, add: PMT × [((1 + r/n)^(nt) - 1) / (r/n)]
The Formula
A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) - 1) / (r/n)]The first part calculates the growth of your initial investment. The second part calculates the growth of your regular contributions. Together they give the total future value of your investment.
| Variable | Meaning |
|---|---|
| A | Final amount (future value) |
| P | Principal (initial investment) |
| r | Annual interest rate as a decimal (e.g., 7% = 0.07) |
| n | Compounding frequency per year (12 for monthly, 1 for annually) |
| t | Number of years |
| PMT | Regular contribution per compounding period |
Common Examples
$10,000 at 7% for 10 years
$19,672
$10,000 at 7% for 20 years
$38,697
$10,000 at 7% for 30 years
$76,123
$5,000 at 10% for 10 years
$12,969
$10,000 + $200/month at 7% for 10 years
$54,714
$10,000 + $500/month at 8% for 30 years
$854,537
What Is Compound Interest?
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest — which only earns interest on your original amount — compound interest creates a snowball effect where your money grows faster and faster over time. Albert Einstein reportedly called it “the eighth wonder of the world,” and while that attribution is disputed, the math behind it is not.
Here is a concrete example: $10,000 invested at 7% simple interest earns $700 per year, every year — $7,000 after 10 years, giving you $17,000 total. With compound interest at the same 7% rate, your money grows to $19,672 after 10 years. That extra $2,672 is interest earned on your interest. Over 30 years, the gap becomes enormous: simple interest gives you $31,000 while compound interest produces $76,123.
The Rule of 72
The Rule of 72 is a quick mental math shortcut for estimating how long it takes your money to double at a given interest rate. Simply divide 72 by the annual interest rate:
- At 6%: 72 ÷ 6 = 12 years to double
- At 7%: 72 ÷ 7 ≈ 10.3 years to double
- At 8%: 72 ÷ 8 = 9 years to double
- At 10%: 72 ÷ 10 = 7.2 years to double
- At 12%: 72 ÷ 12 = 6 years to double
This rule works because of the mathematical relationship between exponential growth and the natural logarithm of 2 (approximately 0.693). The Rule of 72 is most accurate for rates between 6% and 10%, which conveniently covers the range most relevant to long-term investing.
The Power of Starting Early
Time is the most important variable in compound interest. Consider two investors:
- Investor A starts at age 25, invests $200/month at 7% annual return, and stops contributing at age 35 (10 years of contributions, then lets it grow). Total invested: $24,000. By age 65, this grows to approximately $353,000.
- Investor B starts at age 35, invests $200/month at 7% annual return, and contributes for 30 years straight until age 65. Total invested: $72,000. By age 65, this grows to approximately $243,000.
Investor A contributes three times less money but ends up with significantly more — because those early dollars had 40 years to compound. This is why every financial advisor emphasizes starting as early as possible, even with small amounts.
Compounding Frequency: Does It Matter?
Interest can compound at different intervals — annually, quarterly, monthly, daily, or even continuously. More frequent compounding means slightly more growth because interest starts earning interest sooner. Here is what $10,000 at 7% looks like after 10 years with different compounding frequencies:
- Annually (1x/year): $19,672
- Quarterly (4x/year): $19,989
- Monthly (12x/year): $20,097
- Daily (365x/year): $20,137
The difference between annual and daily compounding on $10,000 over 10 years is about $465 — meaningful but not dramatic. The frequency matters much more with larger balances and higher rates. For most practical purposes, monthly compounding (used by most savings accounts and investment platforms) is close enough to daily that the difference is negligible.
Real vs. Nominal Returns: The Inflation Factor
When you see a 7% or 10% return cited for the stock market, that is the nominal return — before adjusting for inflation. The real return subtracts inflation, which has historically averaged about 3% per year in the United States.
This distinction matters enormously over long time periods. At a nominal 7% return with 3% inflation, your real return is roughly 4%. Over 30 years, $10,000 grows to $76,123 in nominal terms but only about $32,434 in today’s purchasing power. Your investment still triples in real terms — but it does not grow nearly as dramatically as the raw numbers suggest.
When planning for retirement or long-term goals, use real returns (typically 4–5% for a stock portfolio) for more realistic projections, or calculate both to see the range.
How 401(k) Matching Supercharges Compound Growth
If your employer offers 401(k) matching, that is essentially free money that compounds alongside your own contributions. A common match is 50% of your contributions up to 6% of your salary.
Consider someone earning $70,000 who contributes 6% ($4,200/year or $350/month). With a 50% match, the employer adds $2,100/year ($175/month). That is $525/month going into the account. At 7% returns over 30 years, this grows to approximately $637,000 — of which about $191,000 came from employer contributions and their compound growth. Not contributing enough to get the full match is literally leaving free money on the table.
Compound Interest on Debt: The Dark Side
Compound interest works against you on debt just as powerfully as it works for you on investments. Credit cards are the most common example: with an average APR of 22% and minimum payments, a $5,000 credit card balance can take over 20 years to pay off and cost more than $8,000 in interest — more than the original balance.
This is why high-interest debt should be eliminated before investing. Paying off a 22% credit card is equivalent to earning a guaranteed 22% return on your money — far better than any investment can reliably deliver. The same compound interest formula that builds wealth in your retirement account is working against you on every unpaid balance.
Mortgages, student loans, and auto loans also compound, but at much lower rates. A mortgage at 6.5% is far less destructive than credit card debt at 22%, which is why financial advisors generally recommend prioritizing high-interest debt while maintaining regular contributions to tax-advantaged retirement accounts.