The math behind recurring deposits
A one-off deposit follows the familiar FV = P(1 + r/n)nt. A stream of monthly deposits needs one more formula, because every deposit starts compounding on its own clock. Summing that series gives the ordinary annuity future value (deposits at the end of each month):
FVdeposits = PMT × ((1 + i)N − 1) / i
PMT is the monthly deposit, i the monthly growth rate (r/12 when compounding is monthly), and N the number of deposits. The calculator adds this to the lump-sum growth and verifies the closed form against a month-by-month simulation to the cent.
Worked example: $500 a month for 20 years
At 6% compounded monthly, i = 0.005 and N = 240 deposits:
- Future value of the deposits: 500 × ((1.005240 − 1) / 0.005) = $231,020.45
- Of that, your own money is $500 × 240 = $120,000.00
- Compound growth supplies the remaining $111,020.45 — almost a dollar-for-dollar match
The chart above makes the same point visually: the orange “total contributed” line is straight, while the blue balance curve bends away from it — slowly in the first years, dramatically in the last. In a 20-year plan, roughly the final third of the timeline produces the majority of the interest, which is why starting early beats starting big.
Two honest caveats
Timing: this tool assumes deposits land at the end of each month. Depositing at the start instead (an annuity due) would add about 0.5% — $1,155.10 in the example above. Real paycheck timing sits somewhere in between, so treat the difference as noise.
Inflation: $231,020 twenty years from now is not $231,020 of today’s purchasing power. Flip on the inflation toggle: at the default 2.5% per year the example deflates to about $140,985 in today’s money — still well above the $120,000 deposited, but a much more truthful picture of a long-horizon plan.
Related calculators
- Compound interest calculator — the full tool with the step-by-step formula guide and FAQ.
- Monthly compound interest calculator — focused on the 12-period formula and APY conversion.
- Daily compound interest calculator — how much extra 365-day compounding really adds.
Frequently asked questions
How is compound interest with monthly contributions calculated?
Two formulas are added together. The starting deposit grows by FV = P × (1 + r/n)^(n×t). The monthly deposits grow by the ordinary-annuity formula FV = PMT × ((1 + i)^N − 1) / i, where PMT is the monthly deposit, i is the monthly growth rate, and N is the number of deposits. Example: $500/month at 6% compounded monthly for 20 years is 500 × ((1.005^240 − 1) / 0.005) = $231,020.45.
Do contributions at the start of the month earn more than at the end?
Yes, slightly — each deposit gets one extra month of growth. This calculator assumes end-of-month deposits (an "ordinary annuity"). Beginning-of-month deposits (an "annuity due") multiply the deposits' future value by (1 + i): for $500/month at 6% over 20 years that adds $1,155.10 to a $231,020.45 result, about 0.5%.
Is it better to invest a lump sum or monthly contributions?
Mathematically, money invested earlier compounds longer, so if you already have a lump sum, investing it immediately maximizes expected time in the market. Monthly contributions are how most people actually save — out of each paycheck — and they also spread out purchase timing. The two answer different questions; this calculator lets you model both at once.
How much do I need to save monthly to reach a goal?
Work backwards by trial: set your years and an assumed rate, then adjust the monthly contribution until the future value crosses your target. Because the annuity formula is linear in the deposit amount, doubling the monthly contribution exactly doubles the deposits' share of the future value — a few tries converge fast.
Educational estimate only — not financial advice. Returns are not guaranteed.