The SIP Calculator Formula, Explained
Type ₹25,000 a month, 12% a year and 10 years into many SIP calculators and you will see about ₹58.08 lakh. Type the same numbers into the Sipculator SIP calculator and you will see ₹56.01 lakh. Neither is broken. Both use the same formula, with one small difference in how they turn an annual return into a monthly one, and here that difference is worth ₹2.08 lakh.
This guide takes the formula apart, works an example by hand, rebuilds it in Excel, and explains which version matches the way mutual fund returns are reported.
The formula
FV = P × [(1 + i)n − 1] ÷ i × (1 + i)
- FV: future value, what the SIP grows to
- P: the monthly instalment
- n: the number of instalments (years × 12)
- i: the monthly rate of return
This is the future value of an annuity due: equal payments made at the start of each period. Each instalment compounds for as long as it stays invested, so the first grows for n months and the last for one. The bracketed fraction adds up all those growth factors, and the final × (1 + i) gives every instalment its extra month for being invested at the start of the month rather than the end.
A worked example: ₹1,000 a month for one year
At 12% a year, the monthly rate is 0.9489% (the next section explains why it is not 1%). Here are the first 3 months:
| Month | Balance after the instalment | Growth during the month | Balance at month end |
|---|---|---|---|
| 1 | ₹1,000 | ₹9.49 | ₹1,009.49 |
| 2 | ₹2,009.49 | ₹19.07 | ₹2,028.56 |
| 3 | ₹3,028.56 | ₹28.74 | ₹3,057.29 |
Carry on to month 12 and the balance reaches ₹12,766: ₹12,000 invested plus ₹766 of growth. The formula gets there in one line: ₹1,000 × [(1.009489)12 − 1] ÷ 0.009489 × 1.009489 = ₹12,766.
Why two calculators disagree: the monthly rate
Fund returns are quoted as compound annual growth (CAGR). A calculator must convert that annual figure into a monthly rate, and there are two common ways to do it:
| Method | Monthly rate at 12% a year | What 12 months compound to | ₹25,000 a month for 10 years |
|---|---|---|---|
| Divide by 12: i = r ÷ 12 | 1% | 12.68% | ₹58,08,477 |
| Compound equivalent: i = (1 + r)1/12 − 1 | 0.9489% | 12% | ₹56,00,897 |
Dividing by 12 is the textbook shortcut, and it is right for rates quoted as nominal and compounded monthly, as many loan rates are. A fund’s “12% CAGR” is not quoted that way. Twelve months at 1% compound to 12.68%, so a calculator that divides by 12 quietly assumes 12.68% when you type 12%.
The gap widens with time. For ₹10,000 a month at 12%:
| Time period | Divide by 12 | Compound equivalent | Overstatement |
|---|---|---|---|
| 10 years | ₹23,23,391 | ₹22,40,359 | ₹83,032 (3.7%) |
| 20 years | ₹99,91,479 | ₹91,98,574 | ₹7,92,906 (8.6%) |
| 30 years | ₹3,52,99,138 | ₹3,08,09,732 | ₹44,89,406 (14.6%) |
When you plan around a fund’s reported CAGR, use a calculator that applies the compound-equivalent rate. The SIP calculator here does, and it prints the formula with your own numbers plugged in, so you can check every step. Otherwise you are measuring a 12% fund against a 12.68% yardstick.
Rebuilding it in Excel or Google Sheets
Both have an FV function: =FV(rate, nper, pmt, [pv], [type]). Enter the instalment as a negative number, since it is money going out, and set type to 1 for start-of-month payments:
- Compound equivalent:
=FV((1+12%)^(1/12)-1, 120, -25000, 0, 1)gives about ₹56,00,897 - Divide by 12:
=FV(12%/12, 120, -25000, 0, 1)gives about ₹58,08,477
Lumpsum and step-up versions
- Lumpsum: FV = P × (1 + r)t, with r the annual rate and t the years. ₹30 lakh invested once for 10 years at 12% grows to ₹93.18 lakh. The same ₹30 lakh spread over 120 monthly instalments grows to ₹56.01 lakh, because on average it is invested for only about half as long. The lumpsum calculator works this way.
- Step-up SIP: each year’s instalments are larger, so calculators usually simulate the plan month by month: grow the balance, add the instalment, and raise it by the step-up rate at the start of each year. That is how the step-up SIP calculator does it.
From projection to reality: XIRR
A calculator projects with one constant rate. A real SIP earns a different return every month, so its actual performance is measured with XIRR, which annualises a series of dated cash flows. List each instalment as a negative amount with its date, add the current value as a positive amount with today’s date, and XIRR returns the rate your SIP has actually earned. That is the number to compare with the rate you planned for.
Frequently asked questions
Is the SIP formula just compound interest?
Yes, applied to each instalment separately and then added up. A lumpsum compounds one amount; a SIP of n instalments compounds n amounts, each for a different number of months.
Why does the formula end with × (1 + i)?
Because SIP instalments are invested at the start of each month. Each gets one more month of growth than an end-of-month payment would.
Which monthly rate should I use for mutual funds?
The compound equivalent, (1 + r)1/12 − 1, because fund returns are quoted as CAGR. Dividing by 12 suits rates quoted as nominal and compounded monthly.
Mutual fund investments are subject to market risks; read all scheme-related documents carefully. The figures in this guide are illustrations that assume a constant return. They are not a forecast or investment advice.