Calculadora de porcentajes

Why compound interest grows so fast

Simple interest pays you only on the money you originally put in. Compound interest pays you on your principal and on the interest you have already earned, so each period's growth is calculated on a slightly larger base than the last. That feedback loop is what turns a steady rate into an exponential curve. The textbook formula for a lump sum is A = P(1 + r/n)^(nt), where P is the principal, r the annual rate as a decimal, n the number of times interest compounds per year, and t the number of years. The (1 + r/n) factor is applied nt times — once per compounding period — and because each application multiplies an already-grown balance, the result climbs far faster than P × r × t ever would.

What this calculator actually computes

This tool goes beyond a single lump sum: it also models regular monthly contributions, which is how most people really save. It steps through the investment one compounding period at a time. In each period it multiplies the current balance by (1 + r/n) and then adds your contribution for that period. The contribution is spread to match the compounding frequency you choose — with monthly compounding it adds your monthly amount each month; with annual compounding it adds twelve months' worth once a year; with daily compounding it adds a small slice each day — so your total yearly contribution is the same regardless of frequency. It then reports four figures: the final value, the total interest earned, the total amount you invested (principal plus all contributions), and a return multiplier equal to final value divided by what you put in. A year-by-year bar chart shows the growing balance against your cumulative contributions.

A worked example

Take the tool's defaults: a $10,000 starting amount, a 7% annual rate, $200 added every month, monthly compounding, over 20 years. The monthly rate is 7% ÷ 12 ≈ 0.583%. Each month the balance is multiplied by 1.00583 and then $200 is added. Over 240 months this produces a final value of roughly $143,000. You contributed $10,000 up front plus $200 × 12 × 20 = $48,000, for $58,000 invested — meaning compound interest alone added about $85,000, and the return multiplier is around 2.5×. Notice that the money you contributed in the early years had two decades to compound, while a dollar added in year 19 barely grew. That is the whole lesson of compounding: time matters more than amount.

The Rule of 72 and compounding frequency

A quick mental shortcut: divide 72 by your annual percentage rate to estimate how many years it takes money to double. At 7%, that's 72 ÷ 7 ≈ 10.3 years to double a lump sum. It's an approximation, but it's close enough to sanity-check this calculator's output. As for how often interest compounds — daily, monthly, quarterly, or annually — more frequent compounding earns slightly more, but the effect is smaller than people expect. The gap between annual and monthly compounding at typical rates is a fraction of a percent of the final balance. Don't chase compounding frequency; chase a higher rate, a longer horizon, and bigger contributions, which dwarf it.

Genuine use cases

• Retirement planning. Model how a monthly contribution to a retirement account grows across 20, 30, or 40 years and see why starting early beats starting big.
• Comparing savings options. Plug in two different rates to see the long-run dollar difference between a 4% and a 5% account — it is larger than the one-point gap suggests.
• Goal setting. Work out roughly what monthly amount reaches a target like a house down payment by a chosen year.
• Understanding debt in reverse. The same math drives compound interest on loans and credit cards working against you — the curve that builds wealth also builds debt.

Common mistakes

• Confusing nominal rate with real return. This tool uses the rate you type. Inflation erodes purchasing power, so a 7% return during 3% inflation is closer to 4% in real terms. The dollar figures are nominal.
• Ignoring taxes and fees. Investment gains may be taxed and funds charge fees; both reduce the effective rate. Enter a rate net of fees for a more honest projection.
• Assuming a constant rate is realistic. Markets fluctuate. A fixed rate is a planning convenience, not a guarantee — use it to understand the mechanics, not to predict an exact balance.
• Underrating early contributions. Because of the long compounding tail, money invested in year one is worth far more at the end than the same amount invested near the finish. Front-load contributions when you can.

All calculations run in your browser; none of the figures you enter are sent anywhere.