How compound growth works
Compound growth is what happens when the returns you earn start earning returns of their own. Instead of growing by the same amount each period, your balance grows by a little more each time, because each period's return is calculated on a larger base than the one before it.
This calculator works the way the money actually moves: it steps through every period one at a time. In each period it adds the return earned on the current balance, then adds your contribution at the end of the period. Doing it period by period — rather than with a single formula — keeps the year-by-year chart honest and handles a 0% rate without any special cases.
The formula
For a single lump sum with no further contributions, the closing balance follows the standard compound interest formula:
A = P(1 + r/n)^(nt)
- A
- — the final amount
- P
- — the starting principal
- r
- — the annual rate as a decimal (5% = 0.05)
- n
- — the number of compounding periods per year
- t
- — the number of years
A worked example
Suppose you start with 10,000 at a 5% annual rate, compounded monthly, for 3 years, with no contributions. Here n = 12 and t = 3:
- r / n = 0.05 ÷ 12 = 0.0041667 per month
- n × t = 12 × 3 = 36 periods
- A = 10,000 × (1 + 0.0041667)^36
- A = 10,000 × 1.16147 ≈ 11,614.72
After 3 years the balance is about 11,614.72 — roughly 1,615 of it earned interest. Add regular contributions and that interest figure grows much faster, because each contribution starts compounding too.
A few things to keep in mind
- Time matters more than the amount. Starting earlier, even with smaller sums, usually beats starting later with more — compounding needs years to do its work.
- The rate you enter is an assumption, not a promise. Real returns vary from year to year; use a conservative figure so the results don't flatter you.
- These numbers ignore inflation, fees, and taxes. A 5% return with 3% inflation is closer to 2% in real terms.
- This tool is for education and awareness, not financial advice.