Compound Interest Calculator

Compound interest is often called the most powerful force in personal finance because, unlike simple interest which only ever grows on the original principal, compound interest earns returns on both the original amount and all previously accumulated interest. This creates a curve that starts slow but accelerates dramatically the longer money is left to grow, which is why time in the market matters as much as, or more than, the interest rate itself. The core formula for compound interest without any additional contributions is FV = P × (1 + r/n)^(nt), where P is the initial principal, r is the annual interest rate (as a decimal), n is the number of times interest compounds per year, and t is the number of years. The "compounding frequency" — annually, semi-annually, quarterly, monthly, or daily — determines how often the interest earned gets folded back into the balance to start earning its own interest. More frequent compounding produces a slightly higher return at the same nominal annual rate, because interest starts compounding on itself sooner; the difference between annual and daily compounding at typical savings rates is usually small (a fraction of a percent over many years) but not zero. Adding regular contributions — a monthly deposit into a savings or investment account — changes the calculation from a single lump sum growing on its own into a combination of a lump sum plus a growing annuity. The exact math for an annuity that compounds at an arbitrary frequency while contributions arrive monthly gets complicated fast, so in practice (and in this calculator) the contribution portion is approximated using a standard monthly-compounding annuity formula, applied consistently regardless of which compounding frequency you selected for the principal. This is a deliberate simplification that keeps the tool accurate for real-world "compound interest plus monthly savings" scenarios without requiring an unwieldy mixed-frequency formula — the approximation is clearly noted beneath the results. A worked example shows the scale of the effect: £10,000 invested at 7% annual interest, compounded monthly, with no further contributions, over 20 years grows to approximately £10,000 × (1 + 0.07/12)^(12×20) ≈ £40,387 — roughly quadrupling without a single additional deposit. Now add a £200 monthly contribution to that same scenario: the contributions alone total £200 × 12 × 20 = £48,000 over the period, but because each contribution also earns compound interest for the remaining years after it's deposited, the contribution portion of the final balance grows to significantly more than £48,000, pushing the total future value well past £145,000 combined — illustrating why "pay yourself first" saving strategies that start early consistently outperform larger contributions started later, purely due to how many years each pound has to compound. A common misconception is that doubling the interest rate roughly doubles your final balance over a long period — it doesn't, because of the exponential nature of the formula. Doubling the rate from 3.5% to 7% over 20 years produces vastly more than double the growth, since the compounding effect itself accelerates at higher rates. Similarly, people often underestimate how much of their final balance in a long-term savings plan comes from interest rather than their own contributions; in the example above, contributions were £48,000 but the total interest earned across both the lump sum and the contributions is well over £87,000 — nearly twice what was actually deposited.