The formula
A = P × (1 + r / n)n × t
- A — the final amount
- P — the principal (what you started with)
- r — the annual rate as a decimal
- n — how many times per year interest is added
- t — the number of years
The exponent is the whole story. Interest is applied n × t times, and each application acts on a balance that already includes all previous interest. That is what makes growth curve upward rather than run in a straight line.
Why compounding frequency matters less than you think
Going from annual to monthly compounding sounds dramatic, but it barely changes the result. At 7% over 20 years, the difference between annual and daily compounding is a fraction of a percent. What actually moves the needle is time and the rate.
The famous shortcut is the Rule of 72: divide 72 by the annual return to get the number of years it takes to double. At 7%, that is about 10 years.
What this calculator leaves out
- Inflation — the nominal balance grows, but its purchasing power grows more slowly
- Taxes — interest is usually taxable in the year it is earned
- Fees — fund fees compound against you just as returns compound for you
- Regular contributions — this models a single lump sum, not monthly deposits
For a rough real return, subtract inflation from the nominal rate before entering it.