How SIP compounding works: formula, example and nominal vs effective

A SIP (systematic investment plan) is a fixed amount invested every month. Each instalment earns the assumed return from the month it goes in, so early instalments grow for longer than later ones. That is what compounding means: growth earns growth.

With an instalment of P, a monthly rate of i and n months, and each instalment going in at the start of its month, the value at the end is:

value = P × [((1 + i)ⁿ − 1) ÷ i] × (1 + i)

The part in square brackets adds up how much one rupee paid every month grows to. The last factor, (1 + i), is there because each instalment goes in at the start of the month, one month earlier than the end.

Take ₹5,000 a month for 10 years, which is 120 instalments and ₹6,00,000 put in. At an assumed 10% a year, the monthly rate is 10% ÷ 12, about 0.8333%. After the first year alone the ₹60,000 you put in has grown to ₹63,351.41. After 10 years the pot is ₹10,32,760.1, of which ₹4,32,760.1 is growth.

Notice how much of that growth arrives late. In the first year the growth is ₹3,351.41, and in the last year it is ₹95,239.3, because by then there is a much larger pot for the return to work on.

Nobody knows the return a fund will deliver. So a calculator asks you to assume one, and the honest way to use it is to try several. The same ₹5,000 a month for 10 years, at three assumed returns:

The amount you invest is the same in every row. Only the assumed return changes, and the gap between the rows widens the longer the period runs. Try other periods and returns in the SIP calculator, which can also compare three returns on one chart.

A yearly return has to be turned into a monthly one, and there are two common ways to do it.

• Nominal: divide the yearly rate by 12. Most Indian SIP calculators do this, so results are easy to compare. Twelve months at this rate add up to slightly more than the yearly figure you typed.
• Effective: pick the monthly rate that adds up to exactly the yearly figure over twelve months. It is the more literal reading of “10% a year”.

At 10% a year the nominal answer is ₹10,32,760.1 and the effective answer is ₹10,07,288. Neither is wrong. They answer slightly different questions, which is why a different result on another website is often just a different convention. Our calculator lets you switch between them and shows both for your numbers.

Our calculation treats each instalment as invested at the start of its month, so it earns a full month of growth in that month. Some calculators assume the end of the month instead, which gives a slightly lower value. Real SIPs are not exactly either: the date your fund buys units depends on your SIP date and the fund's rules.

• Fund charges, exit loads and taxes, which reduce what you keep. See the guide on capital gains tax on shares for the tax side.
• Returns that change from year to year. Real returns are uneven, and the order in which good and bad years arrive changes the outcome.
• Inflation. A rupee in 10 years buys less than a rupee today; the SIP calculator can show the total in today's money.