How a SIP actually works — the math behind the magic

A ₹10,000-a-month SIP, run for 20 years at 12% annual return, grows to ₹91,98,574.

If you’ve ever used a SIP calculator, you may have seen a slightly different number for the same inputs — usually around ₹99,91,479. That ₹8 lakh gap isn’t market volatility or rounding. It’s a quiet disagreement about what “12%” means once you compound it monthly.

Most Indian SIP calculators are honest. A few quietly inflate returns by using a shortcut on the monthly rate. Walking through the math explains which is which — and why brackt’s projection sometimes prints a smaller, more accurate number.

It also explains why a SIP works at all. The “power of compounding” line gets thrown around so often that the actual mechanism behind it goes unexamined. There’s no magic. There’s just an annuity-due formula, a geometric monthly rate, and a quirk about which installments compound the longest.

The formula

Every SIP calculator on the Indian web uses some version of the same equation. Future value of an annuity due:

FV = P × [((1 + i)ⁿ − 1) / i] × (1 + i)

P is your monthly investment. n is the total number of months. i is the monthly rate of return. The trailing (1 + i) is what makes it annuity due rather than ordinary annuity — it says you invest at the start of each month, not the end, so each installment gets one extra month of compounding before redemption.

Most SIP calculators do the timing right. They assume you invest on day 1, not day 30. That’s accurate — your SIP mandate hits your bank account at the beginning of the cycle.

The disagreement is one variable in. What is i?

What “12% annual” should mean

There are two ways to convert a 12% annual return into a monthly rate. Only one of them is mathematically correct.

The simple way: i = 12% / 12 = 1% per month. Easy. Reads naturally. Many SIP calculators use this.

The geometric way: i = (1.12)^(1/12) − 1 = 0.9489% per month. Less intuitive. Requires a calculator with a fractional exponent. This is what Groww uses, and it’s the answer that’s actually consistent with “12% per year.”

The difference is small per month. The difference compounded over 240 months is not.

Compound 1% monthly for 12 months and you don’t get 12%. You get (1.01)^12 − 1 = 12.6825%. So a calculator that uses 1% per month is silently telling you you’d earn 12.68% per year — about 0.68 percentage points more than the 12% it shows on the input form.

Compound 0.9489% monthly for 12 months and you get (1.009489)^12 − 1 = 12.0000%. Exactly 12%. The number you typed.

For a ₹10,000-a-month SIP run for 20 years, the simple-division calculator prints ₹99,91,479. The geometric calculator prints ₹91,98,574. The gap is ₹7,92,905 — about 8.6% of the corpus — and it represents the silent inflation embedded by the simpler math. Not a market move. A choice of formula.

Neither calculator is technically “wrong” — both produce the future value of an annuity due. But only the geometric version means what the input form says. A user who types 12% and reads ₹99.9L thinks they modeled 12%. They modeled 12.68%.

brackt uses the geometric convention. So does Groww. Some calculators, including Zerodha’s published step-up SIP spreadsheet, use simple division. ClearTax sits somewhere in between depending on which tool you open. None of this is a scandal — the simplification was probably defensible when SIP calculators were back-of-envelope tools — but the difference matters once you’re modeling a real decision.

Why rupee-cost averaging is a side effect, not the point

The marketing pitch for SIPs leans on rupee-cost averaging. The story goes: when the NAV is low you buy more units, when it’s high you buy fewer, and over time you average out a better cost than a lump-sum buy.

This is true. It’s also less powerful than it sounds.

Rupee-cost averaging is a risk-reduction mechanism, not a return-amplification one. It smooths out the noise of timing the market. It does not, on average, beat lump-sum investing in a market that trends upward over the long run — which Indian equity has, historically.

What rupee-cost averaging actually does is psychological. It removes the question of when to buy. You buy on the 1st of every month, automatically, regardless of whether the Nifty is at 25,000 or 18,000. The investor who SIPs through a 30% drawdown ends up buying cheap units at exactly the moment a lump-sum investor would have frozen.

The marketing literature exaggerates this. RCA does not “guarantee higher returns.” It guarantees consistent behaviour, which is a different thing — and for most working professionals, the more useful thing.

The actual return engine is the compounding curve, not the averaging.

The compounding curve does most of the work

Here’s the part of SIP math that almost no one writes about clearly.

Your first installment compounds for the full 240 months. Your last installment compounds for one month. Every installment in between sits somewhere on that curve.

For a ₹10,000-a-month SIP at 12% annual return (0.9489% monthly):

• The ₹10,000 you invest in month 1 grows to roughly 10,000 × (1.009489)^240 = ₹98,926 by month 240
• The ₹10,000 you invest in month 60 grows to roughly 10,000 × (1.009489)^181 = ₹55,180
• The ₹10,000 you invest in month 120 grows to roughly 10,000 × (1.009489)^121 = ₹31,287
• The ₹10,000 you invest in month 239 grows to roughly 10,000 × (1.009489)^2 = ₹10,190

The ₹10,000 you put in during year 1 contributes roughly ten times as much to your final corpus as the ₹10,000 you put in during year 20. Same ₹10,000. Different position on the curve.

This is the entire reason “starting early” is the most-repeated piece of investment advice in personal finance. It’s not psychological. It’s not behavioural. It’s that the early installments physically have the most time to compound, and the curve is exponential, not linear. Every additional year of compounding at the start of the SIP is worth more than every additional year at the end.

It’s also the reason a SIP that runs for 25 years isn’t 25% better than one that runs for 20 years. It’s roughly 65% better — for the same monthly amount.

Try the numbers yourself. Open the SIP calculator at ₹10,000/month for 20 years, then bump the tenure to 25 years and watch the corpus go from ₹92 lakh to ₹1.52 crore. Same monthly amount. Just five extra years of the early installments compounding.

Why most “SIP examples” use 12%

If you’ve used three different SIP calculators you’ve probably seen “12%” pre-filled on all of them. That number isn’t a guarantee. It’s roughly the long-run CAGR of the Nifty 50 Total Return Index over the last 20-odd years, before fund expenses and tax.

Real funds underperform their benchmark by 0.5%–1.5% a year, depending on category and expense ratio. Real markets are lumpy — there are five-year stretches at 18% CAGR and five-year stretches at 4% CAGR. The 12% figure works for projections because long-run averages are what compound over a 20-year horizon, but it’s a planning assumption, not a return promise. brackt’s per-fund return-range bands (equity ±3%, hybrid-equity ±2.5%, debt ±1%) exist precisely to make this visible.

A more honest framing: at 12% you’re modeling a long-run Nifty TRI scenario. At 9% you’re modeling underperformance or a flatter market. At 15% you’re modeling a friendly two-decade window. All three are inside the realistic envelope. None is the answer.

What “step-up” actually means

A regular SIP keeps the monthly amount constant for the full tenure. A step-up SIP increases the monthly amount once a year — typically at the 12-month anniversary of the SIP start — by a percentage you choose.

A ₹10,000-a-month flat SIP at 12% over 20 years lands at ₹91.98 lakh.

The same SIP with a 10% annual step-up — ₹10,000 in year 1, ₹11,000 in year 2, ₹12,100 in year 3, and so on — lands at roughly ₹1.95 crore.

More than twice the corpus from the same starting amount. Not because the math is different — it’s the same annuity-due formula — but because you’re feeding bigger installments into the front of the compounding curve every year. Each year’s step-up still has years of compounding ahead of it.

Most working professionals get annual salary increments somewhere in the 7%–10% range. A step-up SIP just channels that increment into investment instead of lifestyle inflation. The dedicated article on step-up SIPs walks through this number more carefully, including when step-up doesn’t make sense.

Two things the formula doesn’t capture

The annuity-due formula is precise about future value in nominal rupees, given a constant return. It doesn’t tell you two things you probably care about.

It doesn’t tell you what those rupees will buy. ₹91.98 lakh in 2046 is not ₹91.98 lakh today. At 6% inflation — the long-run Indian CPI average — that corpus is worth about ₹28.7 lakh in today’s purchasing power. The fantasy is meaningfully smaller than the reality.

It doesn’t tell you how much of it you keep. Equity mutual fund redemption attracts LTCG at 12.5% above the ₹1.25 lakh per-FY exemption under Section 112A. For the ₹92 lakh corpus we keep returning to, that tax bite is real. STT is small enough to ignore at this scale, but income tax is not.

The fact that most SIP calculators stop at the nominal corpus number — without inflation, without tax — is the subject of the next article. It’s also why brackt’s calculator has those toggles. Default to the standard number most users expect, but make the truth one click away.

So what

The SIP formula isn’t magic. It’s compound growth applied to recurring contributions, with a geometric monthly rate, with the front-loaded installments doing most of the heavy lifting.

If you remember three things from this article:

1. A 12% input means 12% only if the calculator uses geometric monthly compounding. Simple-division calculators silently model 12.68%, and the gap shows up as a ~₹8L overstatement on a ₹10K-a-month 20-year SIP.
2. The early installments contribute massively more to the final corpus than the late ones. This is why “start early” is the only advice in personal finance that everyone gives and almost no one explains correctly.
3. Rupee-cost averaging is real but oversold. The point of a SIP isn’t to time the market well — it’s to remove the timing question entirely so you stay invested.

The boring version of the SIP story is also the accurate one. The marketing version is louder and less true.

Frequently asked questions

Is the SIP formula different for different fund types?

The formula is identical for equity, debt, ELSS, hybrid, and gold funds. What differs is the realistic expected return (equity ~12%, debt ~7%, hybrid in between) and the tax treatment on redemption, which is covered in mutual fund taxation. The compounding mechanics don’t change.

Why does the calculator use 240 months for 20 years instead of just 20?

Because the SIP compounds monthly, not annually. Each monthly installment is a separate compounding event. The annuity-due formula needs the period count in the same units as the rate — monthly rate plus monthly count, not annual rate plus annual count.

Should I do SIP or lump sum if I have the money today?

Mathematically, lump sum wins in a market that trends upward — your money compounds for longer. SIP wins behaviourally, because most people don’t actually have the lump sum, or won’t deploy it through a drawdown. For working professionals investing from monthly salary, SIP isn’t really a choice. It’s the structure that matches the cash flow.

Is the geometric monthly rate the same as CAGR?

Yes, in spirit. CAGR is the annualised compounded growth rate of a final value over a starting value. The geometric monthly rate is just CAGR’s monthly equivalent — the rate at which something would have to grow each month, compounded, to deliver the stated annual rate. They’re the same idea, expressed at different time intervals.

Why does the calculator show three return scenarios?

Because a single 12% projection is a planning estimate, not a guarantee. Equity returns over 20 years could realistically land anywhere in a roughly 9%–15% band depending on which two decades you got. The three scenarios (conservative / expected / optimistic) communicate the range honestly without pretending one number is the truth. The dedicated article on the SIP calculator’s thesis covers why this matters.

What’s wrong with using simple-division monthly rate if everyone does it?

Two things. One, it doesn’t mean what the input form says — a user typing 12% with simple division is actually modeling 12.68% effective annual return. Two, the magnitude of the error is meaningful at 20-year horizons (~8% overstatement of corpus). For shorter SIPs or rough estimates, simple division gets you in the right neighbourhood. For long-run decisions involving real money, geometric is the right convention.