See how your savings or investment grows with compounding over time.
A = P (1 + r/n)ⁿ∙ₜ
Where P is your principal, r is the annual interest rate, n is how many times per year interest compounds, and t is time in years.
Useful for students learning finance, and for anyone comparing savings accounts, fixed deposits, or investment products across countries.
Compound interest is often summarized as "interest on interest," but the size of that effect depends heavily on how often the interest is actually added to the balance — the compounding frequency. The same nominal annual rate compounded annually, monthly, or daily produces meaningfully different results over time, because more frequent compounding means each small addition of interest starts earning its own interest sooner. This is why two savings products advertising the same headline rate can quietly deliver different real returns — the one compounding daily or monthly will out-earn the one compounding only once a year, and the gap widens the longer the money stays invested.
This is also the mathematical engine behind the Rule of 72's quick doubling-time estimate: at a steady compounding rate, money roughly doubles in 72 divided by the interest rate (in years), and that approximation is most accurate in the 6%-10% range — the exact formula is ln(2) divided by ln(1 + rate), and the approximation loses accuracy at very low or very high rates. The other underappreciated factor is time itself: because each period's growth builds on a larger base than the last, the absolute rupee or dollar growth in the final years of a long-term investment dwarfs the growth in the early years, even though the percentage rate never changed — which is why starting early consistently outperforms contributing more but starting later.
Yes, and the difference grows with both the interest rate and the time horizon. The same nominal rate compounded monthly rather than annually results in a higher effective annual yield, because interest earned partway through the year starts earning its own interest immediately rather than waiting until year-end. Over long periods this compounds into a meaningfully larger final balance.
The Rule of 72: divide 72 by the annual interest rate to get the approximate number of years to double. It's most accurate for rates between roughly 6% and 10% — at much higher rates it tends to slightly underestimate the actual time required. For precision, use the exact formula: years = ln(2) ÷ ln(1 + rate).
Because each period's interest is calculated on a progressively larger base — the same percentage rate applied to a bigger number produces a bigger absolute gain. This is why long-term compound growth charts show a curve that stays fairly flat for years before rising sharply near the end, even though the underlying rate never changed.
Starting early generally wins over contributing more but starting later, because time is the multiplier compounding needs most — money invested early has more compounding periods to benefit from, even at modest contribution amounts. This is the core reasoning behind most retirement-savings guidance to begin as early as possible rather than waiting for a larger lump sum.