Part of our guide to The 50/30/20 Budget Rule
Compounding is straightforward arithmetic that produces results people find hard to believe, which is why seeing your own numbers matters more than reading about it.
What a starting amount plus regular contributions becomes over time, split into what you put in and what the growth added. That split is the useful output — the moment growth exceeds contributions is the point compounding starts doing more work than you are.
How the calculation works
FV = P(1 + r/m)^(mt) + PMT · [((1 + r/m)^(mt) − 1) / (r/m)]P is the starting amount, PMT each contribution, r the annual rate, m the compounds per year, and t the years. The first term grows the lump sum; the second grows the stream of contributions.
Contributions are treated as made at the end of each compounding period. A zero rate is handled separately, since that formula divides by zero — the answer is simply everything you put in.
What the split tells you
Two figures matter more than the total.
Total contributed is money you supplied. Growth is what the returns added.
Early on, contributions dominate. Over long horizons the relationship inverts, and the balance earns more each year than you add. That crossover is the entire argument for starting early — not because early money is special, but because it has more years to compound.
Try the same total contribution over ten years and over thirty. The difference is not three times.
How to read the result
The rate is an assumption, not a forecast. Run it at several rates. If the plan only works at an optimistic one, it is fragile.
Adjust for inflation if you want real spending power. Subtract expected inflation from your rate — 7% nominal with 3% inflation is roughly 4% real. Over decades this changes the answer enormously, and quoting a nominal figure as if it were purchasing power is the most common way these calculators mislead.
Fees compound too, against you. A percentage point of annual fees does not cost one percent — it compounds over the whole period, exactly as returns do.
Tax is not included. Whether the account is tax-advantaged materially changes the outcome.
Important considerations
Real returns are not smooth. This assumes a constant rate; actual markets deliver sequences of good and bad years, and the order matters if you are withdrawing rather than accumulating.
Treat the result as an illustration of the mechanism, not a projection of your balance. The useful conclusions are directional: starting earlier beats contributing more later, and small differences in rate or fees compound into large differences in outcome.
Related reading
- Compound interest, explained with the actual numbers
- Investing for beginners
- APR vs APY — why two rates describe the same money
- ETF vs mutual fund
This is general information, not financial advice. Returns are not guaranteed — see our disclaimer.
Frequently asked questions
What does compounding frequency change?
How often earnings are added to the balance and start earning themselves. More frequent compounding gives a slightly higher result at the same rate — noticeable at high rates, marginal at low ones.
Should I use a real return or a nominal one?
If you want the answer in today's spending power, subtract inflation from your rate. A 7% return with 3% inflation is roughly 4% in real terms, and that is the honest figure for long horizons.
Why does the growth overtake the contributions?
Because returns compound and contributions do not. There is a crossover point where the balance earns more per year than you add, and reaching it is the whole argument for starting early.
Is 7% a reasonable assumption?
It is a commonly used long-run figure for diversified equities before inflation, and it is an assumption rather than a promise. Try a lower rate and see how much the answer moves.
Does this account for tax or fees?
No. Both reduce real returns, and fees compound against you exactly as returns compound for you. Treat the result as an upper bound.
Sources
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