Compound Interest Calculator: How Money Grows Over Time
Compound interest is one of the most important concepts in personal finance — and one of the least understood. Whether you're growing savings, planning retirement, or paying down debt, knowing how compounding works changes the decisions you make. Small differences in time horizon or interest rate compound into enormous differences over decades.
Simple Interest vs. Compound Interest
The difference is straightforward but the long-term impact is dramatic. Take $10,000 invested at 7% per year for 10 years:
Simple Interest
Interest calculated only on the original $10,000 every year.
$10,000 × 7% × 10 years = $7,000 interest
$17,000
after 10 years
Compound Interest (monthly)
Interest calculated on the growing balance every month.
A = 10000 × (1 + 0.07/12)^(12×10)
$20,097
after 10 years
That's $3,097 extra — purely from interest earning interest. Over 30 years the gap becomes far larger.
The Compound Interest Formula
A = P(1 + r/n)^(nt)
How $1,000 Grows at 5% (Monthly Compounding)
| Time Period | Final Amount | Interest Earned |
|---|---|---|
| 5 years | $1,283.36 | $283.36 |
| 10 years | $1,647.01 | $647.01 |
| 20 years | $2,712.64 | $1,712.64 |
| 30 years | $4,467.74 | $3,467.74 |
Starting principal: $1,000 · Rate: 5% annually · Compounding: monthly
The Rule of 72: Mental Estimation
The Rule of 72 is the fastest way to estimate how long it takes money to double: divide 72 by the annual interest rate. At 6%, money doubles in 12 years. At 9%, it doubles in 8 years. At 4%, it takes 18 years. This shortcut is accurate enough for planning decisions and requires no calculator. It also works in reverse: if you want your money to double in 10 years, you need approximately 72 ÷ 10 = 7.2% annual returns.
Real-World Applications
- • Retirement savings: Starting at 25 vs. 35 makes a massive difference — 10 extra years of compounding can nearly double the final balance
- • Index fund investing: The historical S&P 500 return of ~10% annually means investments roughly double every 7 years
- • High-interest debt: Credit card debt at 20% APR compounds against you — paying it off is the equivalent of a guaranteed 20% return
- • Savings accounts: High-yield savings accounts (4–5% in 2024) compound daily, meaningfully outperforming traditional savings (0.01–0.5%)
See your money grow — run the numbers now
Principal · Rate · Frequency · Time · Year-by-year breakdown · Free
Open Compound Interest Calculator →Frequently Asked Questions
What is compound interest?
Compound interest is interest calculated on both the initial principal and the interest that has already accumulated. Each time interest is added (compounded), the new, larger balance becomes the base for the next interest calculation. This creates exponential growth — your interest earns interest, which earns more interest. It is the opposite of simple interest, which only ever calculates on the original principal. Albert Einstein is sometimes (apocryphally) credited with calling compound interest 'the eighth wonder of the world' — and while the quote may be invented, the math behind it is genuinely powerful.
What is the compound interest formula?
The compound interest formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (starting amount), r is the annual interest rate as a decimal (e.g., 7% = 0.07), n is the number of times interest compounds per year (12 for monthly, 365 for daily), and t is the number of years. For example: $10,000 at 7% compounded monthly for 10 years = 10000 × (1 + 0.07/12)^(12×10) = $20,097. The same amount at simple interest would only be $17,000 — compound interest adds over $3,000 extra.
How often should interest compound?
More frequent compounding means slightly more growth, but the differences shrink at higher frequencies. Annual compounding (n=1) is the baseline. Monthly compounding (n=12) gives noticeably more. Daily compounding (n=365) gives a bit more still, but very little beyond that. The practical impact: $10,000 at 5% for 20 years: annual compounding = $26,533; monthly = $27,126; daily = $27,182. The difference between monthly and daily is just $56 over 20 years — which is why 'daily compounding' in a savings account sounds impressive but delivers only marginal real-world benefit. The rate and time period matter far more.
What is the Rule of 72?
The Rule of 72 is a mental shortcut for estimating how long it takes money to double at compound interest. Divide 72 by the annual interest rate to get the approximate years to double. For example: at 6%, your money doubles in approximately 72 ÷ 6 = 12 years. At 8%, it doubles in 72 ÷ 8 = 9 years. At 12%, in 6 years. The rule works because of the mathematics of logarithmic growth — the exact formula uses ln(2) ≈ 0.693, and 72 is a close enough approximation that's also conveniently divisible by many common interest rates. Use it for quick mental estimates without a calculator.
How is compound interest different from simple interest?
Simple interest calculates interest only on the original principal, every period. Compound interest calculates interest on the principal plus all previously earned interest. With simple interest, $1,000 at 5% earns $50 every year regardless — after 20 years the total interest is exactly $1,000. With compound interest (monthly compounding), the same $1,000 at 5% earns $50 in year one, then slightly more in year two because the balance is now $1,051.16, and so on — after 20 years the total grows to $2,712, generating $1,712 in interest. The longer the time horizon, the more dramatic the difference. This is why starting retirement savings early — even with small amounts — outperforms saving large amounts late.