How SIP returns are calculated

A SIP is not one investment. Twelve months of ₹5,000 is twelve separate ₹5,000 investments, each made on a different date, each compounding for a different length of time.

So work out what each one becomes and add them up. With a monthly rate r and n total instalments, and money going in at the start of each month:

• Instalment 1 compounds for all n months: P(1+r)n
• Instalment 2 compounds for n−1 months: P(1+r)n−1
• …
• Instalment n compounds for 1 month: P(1+r)1

The total is therefore:

FV = P[(1+r)1 + (1+r)2 + … + (1+r)n]

That bracket is a geometric series with first term (1+r) and ratio (1+r). Nothing more exotic than that is going on.

A geometric series with first term a and ratio x over n terms sums to a(xn − 1) ÷ (x − 1). Here a = (1+r) and x = (1+r), so x − 1 = r:

FV = P × (1+r) × [((1+r)n − 1) ÷ r]

Which is the formula, with the factors written in a different order. That is the entire derivation — one geometric series, one standard sum.

Two things fall straight out of it:

• Why r cannot be zero. The division by r breaks down. At a zero rate nothing compounds, so the answer is simply P × n, and any careful implementation special-cases it. Ours does.
• Why n matters more than r. n sits in an exponent while r does not. Doubling the duration does far more than adding two points to the return.

₹5,000 a month, 12% a year, 10 years.

1. Monthly rate. r = 12 ÷ 12 ÷ 100 = 0.01. Note this is a nominal rate divided by 12, which is the standard convention — not the twelfth root of 1.12.
2. Number of instalments. n = 10 × 12 = 120.
3. Growth factor. (1.01)¹²⁰ = 3.300387.
4. Series sum. (3.300387 − 1) ÷ 0.01 = 230.0387.
5. Annuity-due adjustment. × 1.01 = 232.3391.
6. Multiply by the instalment. × 5,000 = ₹11,61,695.

You invested ₹6,00,000. Compounding added ₹5,61,695 — 48% of the final figure. Check it in the calculator.

That step-five factor of (1+r) is where calculators diverge, and almost nobody says so.

• Annuity-due assumes money arrives at the start of each period, so every instalment earns one extra month. This is what a real mandate does, and it is what this site uses.
• Annuity-ordinary assumes money arrives at the end, and drops the (1+r).

The difference in the reference case: ₹11,61,695 against ₹11,50,193 — about 1.00%, which is roughly ₹11,502. Small in percentage terms, real in rupees, and it grows with the term.

So if another calculator gives you a slightly smaller number, this is usually why. Neither is "wrong" — they are answering marginally different questions. Ours is documented on the methodology page so you can tell which you are looking at.

The same answer arrives from a loop that needs no algebra:

value = 0; each month: value = (value + P) × (1 + r)

Run that 120 times and you get ₹11,61,695 — the identical figure, because it is the identical series.

This site computes both, deliberately. The closed form gives the headline number; the loop generates the year-by-year table, and it also handles a step-up SIP, where a changing instalment means there is no clean closed form at all. The test suite asserts the two agree, so the table and the total can never drift apart.