The formula behind every SIP calculator, worked through

The annuity-due formula every SIP calculator runs, worked through with real numbers — plus why a step-up SIP lowers the instalment so sharply.

The short answer: A SIP projection is one formula: the future value of an annuity due, where a fixed instalment is invested at the start of each period and compounds at a monthly rate. Every SIP calculator on the internet, including ours, is running it. Knowing it does two useful things — it lets you check any figure a distributor or app quotes you, and it makes visible the part that matters most, which is that the result is far more sensitive to the number of years than to the size of the instalment.

Key points

Future value of a monthly SIP = P × [((1+i)^n − 1) / i] × (1+i), where i is the monthly rate and n the number of instalments.
The monthly rate is the annual rate divided by twelve, which is the convention Indian SIP calculators use — not the twelfth root.
Time dominates: ten years of contributions started now and then left alone beats twenty years started a decade later — on half the money in.
A step-up SIP raises the instalment a fixed percentage each year. At 10% a year over a 15-year horizon it cuts the starting instalment by about 42%.

The formula

A SIP projection is a single closed-form expression. Every SIP calculator you will find, including the one on this site, evaluates it — there is no proprietary model involved and nothing that requires trusting the tool.

Future value of a monthly SIP (annuity due): FV = P × [ ((1 + i)ⁿ − 1) ÷ i ] × (1 + i)

P — the monthly instalment.
i — the monthly rate, taken as the annual rate ÷ 12. This is the convention Indian SIP calculators use; it is not the twelfth root of the annual rate, and the two differ slightly.
n — the total number of instalments (years × 12).
The trailing (1 + i) makes it an annuity due: each instalment is invested at the start of the month, so it earns one extra month of growth compared with an ordinary annuity.

Rearranged for the instalment rather than the outcome, it answers the more useful question — what do I need to put in each month to reach a target?

Instalment required for a target: P = (FV × i) ÷ [ ((1 + i)ⁿ − 1) × (1 + i) ]

This is exactly what the Reverse Goal Planner solves.

Worked through, step by step

₹10,000 a month for 10 years at an assumed 12% a year.

₹10,000 monthly, 120 instalments, 12% a year

Monthly rate i: 0.12 ÷ 12 = 0.01
n: 10 × 12 = 120
(1 + i)ⁿ: 1.01¹²⁰ = 3.30039
((1.01¹²⁰ − 1) ÷ 0.01): 230.039
× P: ₹23,00,387
× (1 + i): ₹23,23,391
Total contributed: ₹12,00,000

Growth of ₹11,23,391 on ₹12,00,000 contributed. You can reproduce every line of this on any calculator, which is the point of publishing it.

Why time dominates the instalment

The formula has an exponent in it, and everything follows from that. The most direct way to see it is to compare two people who invest the same amount each month at the same rate, and differ only in when they do it.

Both invest ₹10,000 a month at 12%. Balance measured at year 30.
	Contributes	Total put in	Value at year 30
Started immediately	Years 0–10, then stops and leaves it	₹12,00,000	₹2,53,07,659
Waited ten years	Years 10–30, without missing a month	₹24,00,000	₹99,91,479

Assumes 12% a year throughout, which no real market delivers smoothly. The comparison between the two is the robust part, not either absolute figure.

The person who contributed half as much, and stopped twenty years earlier, ends with more than two and a half times as much. Nothing about their fund selection or their discipline differed — only the number of years their earliest instalments had to compound.

The step-up SIP, and how much it changes

A step-up SIP raises the instalment by a fixed percentage each year on the assumption that your income rises too. FinatriX models 10% a year. There is no closed form for the instalment it requires, so the planner simulates the full schedule month by month and binary-searches for the starting instalment that lands on the target.

Reaching ₹1 crore in 15 years at 12%

Flat SIP throughout: ₹19,819 per month
Step-up SIP, starting instalment: ₹11,516 per month
Reduction in the starting instalment: ≈ 42%
Instalment in the final year: ₹11,516 × 1.10¹⁴ = ₹43,732

The step-up almost halves what you have to find in year one, and pays for it with much larger instalments later — by design, on the bet that your income grows faster than 10% is painful.

That bet is the whole decision. If your income genuinely rises, a step-up is strictly better because it front-loads affordability into the years when money is tightest. If your contribution has to stay flat, the schedule will break in year six or seven, and a flat SIP you can actually maintain is the better plan.

Reverse Goal Planner: Enter a target and a horizon to see the required instalment across all three modelled return paths, with the step-up figure beside each.

Adjusting the target for inflation

A target expressed in today's rupees is not the amount you will need. A ₹1 crore goal fifteen years out has to be grown to what it will cost by then before the instalment is solved, or the plan is systematically under-funded from the first month.

Inflation-adjusted target: target at maturity = target today × (1 + inflation)^years

FinatriX uses 6% for this adjustment, applied before the instalment is solved.

What ₹1 crore in today's money costs in 15 years at 6%

Target in today's rupees: ₹1,00,00,000
1.06¹⁵: 2.39656
Target at maturity: ₹2,39,65,582
Flat SIP required at 12%: ₹47,496 per month, against ₹19,819 unadjusted

The instalment more than doubles. This is the single largest correction most goal plans are missing, and it grows with the horizon — which is exactly the case where people are most confident their number is fine.

What the formula cannot tell you

It assumes a constant rate. Real returns arrive in an order, and the order matters enormously near the end of a horizon, when the balance is largest.
It assumes you never miss a month. Interrupted contributions are the most common reason real goals miss, and no formula models them.
It says nothing about which assets deliver the rate you assumed. That is an asset allocation question, and it is where the risk actually lives.
It ignores costs. An expense ratio of 1% a year removes a meaningful share of a 25-year outcome, and it is subtracted from the rate you plugged in.

None of that makes the projection useless. It makes it a comparison tool rather than a prediction — the difference between two scenarios is far more trustworthy than either absolute figure, which is the same caution that applies to every projection on this site.

Frequently asked questions

How is SIP return calculated?

With the future-value formula for an annuity due: each instalment compounds for the number of months remaining after it is invested, and the total is the sum of those. In closed form it is P × [((1+i)^n − 1) / i] × (1+i). The trailing (1+i) is what makes it an annuity due — it accounts for each instalment being invested at the start of the month rather than the end.

What is a step-up SIP and how much does it help?

A step-up SIP raises the contribution by a fixed percentage each year — FinatriX models 10% — on the assumption that income rises too. Over a long horizon it lowers the starting instalment needed to reach a given target substantially, because the later, larger instalments do a disproportionate share of the work. It suits a rising income and is the wrong choice if your contribution has to stay flat.

Does a SIP guarantee a return?

No. A SIP is a payment schedule and carries the full risk of whatever it invests in. An equity SIP can be down 30% or more in a bad year and can end a five-year period below the amount contributed. What it does reliably do is average your entry price and remove the timing decision — which is worth a great deal, but is not a guarantee.