How this instrument works
This is the plain, unwrapped version of the compounding formula that sits underneath a taxable brokerage account, a robo-advisor projection, or the back-of-envelope math someone runs before opening any specific account at all. Two streams of money grow side by side: Starting principal, $ behaves like an ordinary lump sum, multiplied by the same monthly growth factor for the entire span, while Monthly contribution, $ is a fresh deposit added every month that only earns however many months are left to run before the horizon ends. A dollar contributed in month one compounds for nearly the whole stretch; a dollar contributed in the final month barely earns anything before the clock stops.
The formula converts Assumed annual return, % into a monthly rate by dividing by 1200 rather than 100, because the return is quoted per year but the contribution arrives every month, and both pieces need to run on the same monthly clock before they can be added together. That monthly rate, g, gets raised to the power of total months elapsed to grow the principal, and folded into a second term — the future value of a level monthly deposit series — to grow the contribution stream. Neither piece is optional: set Monthly contribution, $ to zero and the second term vanishes on its own, leaving pure lump-sum growth.
What sets this apart from the account-specific calculators elsewhere on this site is what it deliberately leaves out. A 401(k) or 403(b) sheet bolts on an employer match and an IRS contribution ceiling; a 529 sheet assumes an enrollment date and ignores state tax deductions; an EPF sheet derives the deposit from a mandatory statutory rate. This one attaches none of that — no cap, no match, no lock-in, no account-specific tax treatment — because it is meant for the moment before any of those rules apply: sizing a plain brokerage plan, comparing what a bigger monthly habit does against a bigger starting balance, or checking a number someone else quoted you.
- Enter what you already have invested, or are ready to deposit today, under Starting principal, $.
- Set Monthly contribution, $ to the amount you plan to add every month from now until the end of the horizon.
- Type the growth rate you're assuming into Assumed annual return, % as a plain percentage — 7 for seven percent, not 0.07.
- Set Investment horizon, years to how long the money stays invested, then read Projected future value for the combined result.
Worked example — $10,000 plus $200 a month for 20 years
Take the default sheet: Starting principal, $ at 10000, Monthly contribution, $ at 200, Assumed annual return, % at 7, and Investment horizon, years at 20. The monthly rate is g = 7 ⁄ 1200 = 0.005833, and the horizon runs n = 240 months. Feeding those into the formula gives Projected future value of $144,572.72 — nothing rounded, nothing estimated.
Split the two streams and each half is checkable on its own. The $10,000 starting principal alone compounds to $40,387.39 over those 240 months — the identical arithmetic a lump-sum-only projection would return for that piece by itself. The $200-a-month stream adds up to $48,000 of actual deposits across 240 payments, yet contributes $104,185.33 to the total, more than double what was physically put in, because early monthly deposits ride nearly the full 20 years of growth while the last few barely have time to earn anything before the horizon ends.
Questions
Why does the monthly contribution end up worth more than what I actually deposited?
Because each month's deposit is a separate sum that only compounds for whatever time is left, not the whole horizon. On the default sheet, $200 a month for 20 years totals $48,000 in actual deposits, yet grows to $104,185.33 inside Projected future value — the gap is growth on money that, on average, sat for roughly half the full 20 years, since deposits made early ride nearly the entire stretch while later ones barely earn a thing.
What does Assumed annual return, % actually assume?
One smooth, unchanging monthly rate applied identically every single month for the whole horizon — g stays fixed at r ⁄ 1200 from month one through the last. No real brokerage account, index fund, or robo-advisor portfolio delivers a return that flat; actual returns arrive as a bumpy sequence of up and down years that happens to average out near a figure like this, if you're fortunate in when the down years land.
How is this different from the 401(k), 403(b), 529, or EPF calculators on this site?
Those calculators run the same underlying compounding math but bolt on rules specific to one account type — an employer match, an IRS contribution ceiling, a statutory deposit rate, or a fixed enrollment date. This sheet carries none of that. It is the bare formula, useful for a plain taxable brokerage account, a rough back-of-envelope plan, or checking a number someone else has quoted you before you commit to any single account type.
Why does a 40-year horizon produce almost five times the value of 20 years, not double?
Because the exponent in (1+g)ⁿ grows the balance geometrically, not in a straight line. Holding every other default the same, 20 years reaches $144,572.72 while 40 years reaches $688,076.79 — 4.76 times as much, not twice as much. Most of that extra growth happens in the second half of the stretch, which is the arithmetic reason starting a decade earlier tends to matter more than adding a larger monthly amount later.
What happens if I set Monthly contribution, $ to zero?
The contribution term collapses to zero on its own, since anything multiplied by zero deposits is zero, leaving pure lump-sum compounding: Starting principal, $ of 10,000 at the default 7 percent for 20 years then reads exactly $40,387.39. That number is a useful check — it is the entire contribution-free portion already embedded inside the combined $144,572.72 default result.
Should I treat Projected future value as a promised outcome?
No — read it as what a fixed, unchanging rate would deliver, not a forecast. The figure is nominal and pre-tax: it ignores brokerage fees, fund expense ratios, capital-gains tax due whenever gains are realized, and inflation eroding whatever survives. Market-based returns also carry real risk of loss that a single assumed percentage cannot show. Treat the output as a planning reference point, not a guarantee of what any account will actually hold.
References
- SEC Investor.gov — investing basics, compounding, and free calculators
- IRS Topic no. 409 — Capital gains and losses
- Federal Reserve — H.15 selected interest rates
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.