How to calculate compound interest
Updated on June 18, 2026 · by Rafael Rossi
Compound interest is "interest on interest": each period, the return is calculated on the full accumulated balance, not just the initial amount. That makes growth exponential — slow at first, then faster and faster.
The formula
Amount = Principal × (1 + i)n
Where i is the rate per period (decimal) and n the number of periods. With monthly contributions, add:
+ PMT × [((1+i)n − 1) / i]
Step-by-step example
$1,000 initial + $300/mo at 0.8%/mo:
| Time | Invested | Balance |
|---|---|---|
| 1 year | $4,600 | $4,863 |
| 5 years | $19,000 | $24,600 |
| 10 years | $37,000 | $62,667 |
Notice: the first 12 months add ~$263 of interest; years 5–10 add over $20,000. Time matters more than the rate.
Common mistake: yearly to monthly rate
Don't divide by 12. Use compound equivalence: i_monthly = (1 + i_yearly)1/12 − 1. E.g., 10%/yr = 0.797%/mo (not 0.833%).
What the math leaves out
Taxes on gains, management fees and inflation. To think in purchasing power, use a real rate (net of inflation).
FAQ
How long until my money doubles? Rule of 72: divide 72 by the rate. At 0.8%/mo, ~90 months.
Bigger contributions or a higher rate? Short term, contributions win; over 10+ years, rate and time take over.