Almost every long-term plan involves both a starting sum and a recurring deposit, yet most explanations of compound interest only cover the starting sum. The combined formula is not difficult, and understanding it changes how you read every projection you will ever see.
This guide builds the calculation from first principles, works a full example with realistic figures, and shows how sensitive the outcome is to each input.
The Two Engines Inside the Formula
A portfolio that receives regular deposits is really two calculations added together. The first is the lump sum you already hold, compounding untouched. The second is a stream of deposits, each one compounding for a different length of time — the deposit made in month one has almost the full horizon to grow, while the final deposit has none.
FV = P(1 + r/n)nt + PMT × [((1 + r/n)nt − 1) ÷ (r/n)]
Where P is the starting balance, PMT the recurring deposit, r the annual return as a decimal, n the number of compounding periods per year, and t the number of years. The first term handles the lump sum; the second is the future value of an ordinary annuity, which is simply a compact way of summing every individual deposit's growth.
A Full Worked Example
Take a $10,000 starting balance, $500 invested monthly, an 8% annual return and a 30-year horizon, compounded monthly.
- Periodic rate: r/n = 0.08 ÷ 12 = 0.006667
- Number of periods: n × t = 12 × 30 = 360
- Growth factor: (1.006667)360 = 10.9357
- Lump sum term: $10,000 × 10.9357 = $109,357
- Annuity term: $500 × [(10.9357 − 1) ÷ 0.006667] = $500 × 1,490.4 = $745,180
- Total future value: $854,537
Deposits over the period total $180,000, and the initial balance was $10,000. Everything above $190,000 — about $664,000 — is compound growth. That ratio is the entire argument for starting early.
How the inputs compare
Each row below changes one variable from the base case of $500 a month for 30 years at 8% (no starting balance), so the effect of each lever is directly comparable.
| Change from base case | Total deposited | Final value | Growth |
|---|---|---|---|
| Base: $500/mo, 30y, 8% | $180,000 | ~$745,000 | ~$565,000 |
| Deposit doubled to $1,000 | $360,000 | ~$1,490,000 | ~$1,130,000 |
| Horizon cut to 20 years | $120,000 | ~$294,000 | ~$174,000 |
| Horizon extended to 40 years | $240,000 | ~$1,745,000 | ~$1,505,000 |
| Return reduced to 6% | $180,000 | ~$502,000 | ~$322,000 |
Doubling the deposit doubles the result exactly, because the annuity term is linear in PMT. Extending the horizon by a third, from 30 to 40 years, more than doubles it — time is the only input with an exponent attached.
You can run your own combination of starting balance, deposit, rate and horizon through the compound interest calculator and see the year-by-year balance curve.
Using the Numbers Honestly
A projection is a model, not a forecast. Three adjustments keep it useful rather than misleading.
- Pick a conservative return. A globally diversified equity portfolio has historically returned roughly 9-10% nominal, but a 7% assumption leaves room for disappointment. Over 30 years the difference between assuming 7% and 10% is enormous, and only one of those errors is recoverable.
- Subtract inflation to read in today's money. Using a real return — roughly your nominal assumption minus 2-3% — produces a figure whose purchasing power you can actually picture. $745,000 in 2056 buys considerably less than it does today.
- Subtract costs. Fund fees and platform charges come directly off the return. A 1% annual fee on the base case removes around $150,000 over 30 years.
What the curve actually looks like
Balances grow almost linearly for the first decade, which is the stage where most people quit. In the base case the balance passes $91,000 at year 10 and $294,000 at year 20, then adds over $450,000 in the final decade alone. Nothing changes in the plan during that time; the balance simply becomes large enough that 8% of it exceeds the annual contributions.