Compound Interest Calculator
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See exactly how your money grows with compound interest: pick any compounding frequency and watch what time does to the balance.
Quick answer: Compound interest grows your money using A = P(1 + r/n)^(nt), where interest earns interest on top of interest. $10,000 at 8% compounded monthly reaches $49,268 after 20 years with no further deposits, more than 4.9× the original amount, entirely from compounding (formula per standard financial mathematics).
📐 Compound Interest Formula
A = $10,000 × (1 + 0.08/12)^(12×20)
A = $10,000 × (1.006667)^240
A = $10,000 × 4.9268 = $49,268
How to Use the Compound Interest Calculator
Enter your starting principal
Input your initial investment or savings balance. Even a modest starting amount compounds significantly over long horizons.
Set a monthly contribution
Add a regular monthly contribution. Pairing a starting balance with steady contributions grows money far faster than either one alone.
Choose compounding frequency
Daily compounding (standard for savings accounts) produces slightly more interest than annual. The difference is small but adds up over decades.
Adjust the time horizon
Compare 10, 20, and 30 year outcomes. The curve bends sharply upward in later years; long time horizons are compound interest's biggest lever.
Add an optional inflation rate
Enter an expected annual inflation rate to see the future value in today's purchasing power alongside the nominal figure.
What Is Compound Interest and How Does It Work?
Compound interest is calculated on both your original principal and the interest that principal has already earned. Einstein is often credited with calling it the "eighth wonder of the world." He probably never said it, but the math backs up the reputation: interest earns interest, which earns more interest, and wealth compounds faster the longer you leave it alone.
Formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual rate, n is the compounding frequency, and t is the time in years.
Does Compounding Frequency Actually Matter?
| Compounding | Times/Year | $10,000 at 5% after 10 years |
|---|---|---|
| Annually | 1 | $16,289 |
| Quarterly | 4 | $16,436 |
| Monthly | 12 | $16,470 |
| Daily | 365 | $16,487 |
Daily compounding earns about $200 more than annual compounding over 10 years on $10,000. That's real money on larger sums and longer timeframes. Most savings and investment accounts compound daily or monthly by default.
The Rule of 72: Quick Mental Math for Doubling Time
The Rule of 72 estimates how long it takes to double your money: divide 72 by the annual interest rate. At 6%, that's 72 ÷ 6 = 12 years. At 8%, 9 years. At 4%, 18 years. It stays accurate for rates between 4–20%, which covers most real-world savings and investment scenarios.
Compound Interest vs Simple Interest
Simple interest is calculated only on the principal: I = P × r × t. Compound interest calculates on principal plus whatever interest has already accrued. Over a year or two the gap is small. Over decades, it's enormous. $10,000 at 7% simple interest for 30 years grows to $31,000. At 7% compound interest, it reaches $76,123, more than double. Run the numbers on a simple-interest loan or bond directly in the Simple Interest Calculator.
How Regular Contributions Change the Math
Adding a regular monthly or annual contribution accelerates growth sharply. Investing $500/month at 7% for 30 years (monthly compounding, matching the calculator's own default above) results in about $610,000, from just $180,000 in total contributions. The remaining roughly $430,000 came entirely from compound interest. If you start 10 years earlier, the final number can nearly double. Time in the market, not timing the market, is what does the heavy lifting. Deciding between a 15-year and 30-year mortgage comes down to the same trade-off: a smaller required payment freed up to invest versus a guaranteed, debt-free return. Compare the two directly in the 15 vs 30 Year Mortgage Calculator.
How Compounding Frequency Changes Your Return: Worked Example
Deposit $10,000 at a 5% nominal annual rate for 10 years and vary only how often interest compounds, using A = P(1 + r/n)ⁿᵗ.
- Annual (n=1): $10,000 × 1.05¹⁰ = $16,288.95
- Monthly (n=12): $10,000 × (1 + 0.05/12)¹²⁰ = $16,470.09
- Daily (n=365): $10,000 × (1 + 0.05/365)³⁶⁵⁰ = $16,486.65
Moving from annual to daily compounding adds $197.70 over ten years on the same nominal rate. Real, but modest. It's also why comparing accounts by nominal rate alone can mislead: a 5.00% account compounded daily slightly out-earns a 5.05% account compounded annually, exactly what APY (annual percentage yield) exists to normalize.
How Much Do Regular Contributions Change the Outcome?
What does adding $200 a month do to the ten-year total?
Layering $200 in monthly contributions onto the $10,000 lump sum above (still 5%, monthly compounding) adds a second future-value-of-annuity term: $200 × [(1.004167¹²⁰ − 1) ÷ 0.004167] ≈ $31,056 in contributed growth, bringing the ten-year total to roughly $47,500 versus $16,470 without contributions. The deposits, not the rate, drove most of that difference. That's the central lesson of long-horizon compounding: consistent contributions usually beat chasing an extra percentage point of return.
Is the Rule of 72 accurate enough to use?
Dividing 72 by the rate estimates doubling time: at 7%, 72 ÷ 7 ≈ 10.3 years. The exact answer from ln(2) ÷ ln(1.07) is 10.24 years. The rule stays accurate to within a few weeks in the 4–10% range typical of long-term investing, which is why it's reliable for a quick mental check without reaching for a calculator.
Why does starting a decade earlier matter more than the rate?
A one-time $10,000 deposit at 7% for 40 years grows to about $149,745. The same deposit for 30 years, started a decade later, reaches only about $76,123, nearly half, despite an identical rate. The missing decade of compounding causes that gap, not a worse return, which is why the calculator's time-horizon field usually moves your projected total more than the rate field does. That's the power of an extra decade of compounding, and it's also where this calculator's job ends: it only models the accumulation phase. Once you're ready to plan how a balance like this gets drawn down in retirement, the Retirement Calculator picks up from here.
Frequently Asked Questions
Sources & Methodology
The compound interest formula follows standard financial mathematics. For further reading and independent verification, see: