Personal finance
Compound interest calculator
Enter three out of four values: the field you leave blank is calculated automatically.
When to use the compound interest calculation
Compound interest applies whenever the interest accrued in one period is added to the capital and, from the next period on, starts earning interest itself. It's the mechanism behind savings accounts, bonds with reinvested coupons, accumulation plans and, on the flip side, unpaid debt (revolving credit cards, overdrafts).
Unlike simple interest, where returns grow linearly, compound interest produces exponential growth: the longer the time horizon, the wider the gap between the two methods. That's why it's the right tool for evaluating multi-year investments, while simple interest remains more suitable for short-term operations.
Numeric example: a capital of €10,000 invested at 3% annually for 10 years, with annual compounding, produces a final amount of 10,000 × (1 + 0.03)^10 ≈ €13,439.16, i.e. €3,439.16 in interest. With simple interest, at the same rate and duration, the interest would have been exactly €3,000: the €439.16 difference comes from compounding the interim interest.
Common mistakes
- Confusing the nominal annual rate with the effective rate when compounding isn't annual (e.g. monthly): in that case both the number of periods and the rate per period need to match the compounding frequency.
- Entering the rate as a whole number rather than a percentage, and forgetting to state it on an annual basis when periods are expressed in years.
- Forgetting that the calculation assumes a constant rate for the whole duration: rate changes over time require calculating each sub-period separately.
Frequently asked questions
What's the difference between simple and compound interest?
With simple interest, interest is always calculated on the initial capital, so it grows linearly. With compound interest, accrued interest is added to the capital each period and itself earns interest, producing exponential growth.
How is the final amount calculated with compound interest?
Using the formula M = C × (1 + i)^t, where C is the initial capital, i is the interest rate per period expressed as a decimal, and t is the number of periods.
Can I calculate the rate or duration instead of the final amount?
Yes: this calculator automatically solves for whichever field you leave blank — capital, rate, number of periods or final amount — using the other three values.
Does the result account for inflation or taxes?
No, the calculation is purely mathematical on nominal capital. For a net real return you need to separately subtract the effect of inflation and the tax treatment applicable to the type of investment.
How this calculation works
The compound interest formula is M = C × (1 + i)^t, where M is the final amount, C is the initial capital, i is the interest rate per period (as a decimal, e.g. 3% = 0.03) and t is the number of periods. Solving the same formula for the other variables gives: C = M / (1 + i)^t, i = (M / C)^(1/t) − 1, t = ln(M / C) / ln(1 + i).
Related calculators
Simple interest
Solve for capital, rate, periods or final amount when interest is not capitalised.
Equivalent simple rate
Convert a simple rate between monthly, quarterly, four-monthly and annual periods.
Equivalent compound rate
Convert a compound rate between frequencies with the exponential formula.
Annuity future value
How much you accumulate paying a constant instalment for n periods at a given rate.