Capital with compound interest
v1capitaltasaanioscapital_finalHow it is worked out
See what a sum grows to when it earns an annual return over several years and the gains are reinvested.
Compound interest reinvests what it earns: each year pays a return on the original capital and on the interest already accumulated, so growth is a curve rather than a straight line. That is why the term is an exponent and not a multiplier.
The expression that runs
capital * (1 + tasa / 100) ^ aniosThe fields arrive with an example filled in: put your own numbers in and run it again. You can also edit the formula to fit your case.
What if the formula were yours?
This calculator is not hand-written: it is an Axioma formula. Open it in the editor to see how it is built, adapt it to your case and create the ones you need.
How the capital grows, year by year
An 8 % annual return becomes a factor of 1.08, and the term enters as an exponent: 1.08 to the power of 10 is 2.1589. Five million therefore grows to 10,794,625 over ten years without a single further contribution.
The exponent is what separates compound from simple interest. If the interest were never reinvested, ten years at 8 % would add 4 million and leave the capital at 9; reinvested, the result is almost 11.
Why the curve steepens at the end
The first year earns 400,000, which is 8 % of five million. The tenth earns almost 800,000, because by then the 8 % is charged on a balance approaching ten million. The money of the final years does most of the work.
That is why time matters more than the rate over long horizons, and why starting early with little usually beats starting late with a lot.
The rule of 72, and inflation
To know when a sum doubles, divide 72 by the rate: 72 over 8 is nine years, and in the example the capital doubles just past the ninth. It is a mental approximation, good enough to compare options without a calculator.
The result is nominal: it is money ten years from now, not money today. If inflation averages 5 %, the real return is closer to 3 %, and over ten years that difference changes the conclusion entirely.
Frequently asked questions
- What if I add money every month?
- This formula is for a sum left alone. Regular contributions need a different one, the future value of an annuity, and that is exactly the kind of calculation you can write in the Axioma editor starting from this one.
- Is the rate I type the effective annual rate?
- Yes: here interest compounds once a year, so the number in the field is an effective annual rate. If your product compounds monthly, the real result comes out slightly higher.
- Why does my bank pay me less than this?
- Because withholding, management fees and taxes come off the gross return. This calculation shows the growth before all of that.