Free compound interest formula calculator
Apply the compound interest formula A = P(1 + r/n)^(nt) — enter principal, rate, compounding periods, and time for future value, updated live, as you type.
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Hypothetical projection. Excludes taxes, inflation, and fees. Actual investment returns vary.
Results are estimates. Consult a professional.
How the compound interest formula works
The compound interest formula is a single expression that handles every combination of lump-sum deposits and recurring contributions at any compounding frequency. Understanding its structure makes it easy to apply to savings accounts, retirement projections, investment portfolios, and loan amortisation alike.
The formula has two additive terms: the lump-sum term, which grows an initial deposit forward in time, and the annuity term, which accumulates the future value of a series of equal periodic payments. Either term can be zero — making the formula general enough to cover both scenarios.
Worked example: $2,000/year at 8% compounded annually for 10 years
Sam invests $2,000 at the end of every year in an account paying 8% annually, compounded annually. There is no initial lump sum. After 10 years the account holds $28,973. Sam paid in $20,000 total; compounding added $8,973.
Future value of annual contributions at various rates
The table shows what a consistent annual contribution grows to over 10, 20, and 30 years at three common rates, using annual compounding and end-of-period deposits. No initial lump sum is included.
| Annual contribution | Rate | 10 years | 20 years | 30 years |
|---|---|---|---|---|
| $1,200 | 6% | $15,817 | $44,143 | $94,870 |
| $1,200 | 8% | $17,384 | $54,914 | $135,940 |
| $1,200 | 10% | $19,125 | $68,730 | $197,394 |
| $2,400 | 6% | $31,634 | $88,286 | $189,740 |
| $2,400 | 8% | $34,768 | $109,828 | $271,880 |
| $2,400 | 10% | $38,250 | $137,460 | $394,788 |
| $6,000 | 6% | $79,085 | $220,714 | $474,349 |
| $6,000 | 8% | $86,919 | $274,570 | $679,699 |
| $6,000 | 10% | $95,625 | $343,650 | $986,964 |
| $12,000 | 6% | $158,170 | $441,427 | $948,698 |
| $12,000 | 8% | $173,838 | $549,140 | $1,359,398 |
| $12,000 | 10% | $191,250 | $687,299 | $1,973,928 |
Annual contributions, end-of-period deposits, annual compounding. Source: Corporate Finance Institute compound interest formula methodology.
Tips for applying the compound interest formula
Knowing the formula is useful; knowing how to apply it correctly in real situations is even more so. These tips cover the most common points of confusion.
- Match contribution frequency to compounding frequency — if you contribute monthly but compound annually, the formula slightly overstates the result. For accuracy, set n equal to your actual payment frequency when rates and contributions are on the same schedule.
- Use annuity-due when deposits fall at the start of each period — some retirement accounts pull contributions at the beginning of each month. The annuity-due version adds one period of growth to the PMT term, producing a slightly higher result.
- Solve backwards to find the required contribution — rearrange for PMT to find how much you need to save each period to hit a target FV: PMT = FV × (r/n) / ((1 + r/n)^(n×t) − 1).
- Separate the two terms to understand each driver — compute the lump-sum term and the PMT term separately to see how much of the final balance comes from the initial deposit versus ongoing contributions.
- Use real rates when comparing against inflation — subtract the expected inflation rate from the nominal rate (approximately) to estimate real purchasing-power growth rather than nominal growth.
Accuracy and limitations
This calculator applies the exact closed-form compound interest formula. It assumes a constant interest rate, fixed equal periodic payments made at the end of each compounding period, and no taxes, fees, or inflation adjustments. It does not model variable contributions, irregular deposits, or rate changes. Real-world investment accounts are subject to market fluctuation, management fees, tax on gains, and changing contribution patterns — all of which will alter actual outcomes.
Results are for educational and planning purposes only and do not constitute financial advice. Consult a qualified financial adviser before making investment or savings decisions.
Compound interest formula terms defined
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