SIP vs Lump Sum: The Maths Behind Which One Ends Up Ahead

"Should I invest it all now or spread it out with a SIP?" is one of the most common questions anyone with a bonus, an inheritance or a maturing FD asks. The honest answer depends on what returns do after you invest, which nobody knows in advance. What you can know is the maths. This guide works through the SIP formula, compares SIP and lump sum on the same money, and then runs three return paths to show when each approach comes out ahead.

The SIP formula, explained

A SIP (systematic investment plan) puts a fixed amount into a mutual fund every month. Each instalment then grows for however many months are left. Adding all those growing instalments up gives the future value of an annuity. Because SIP money usually goes in at the start of each period, calculators use the "annuity due" version, which has an extra (1 + r) at the end:

Take ₹10,000 a month for 10 years at an assumed 12% a year. Then r = 0.12 ÷ 12 = 0.01 and n = 120. (1.01)¹²⁰ is about 3.3004. So FV = 10,000 × (2.3004 ÷ 0.01) × 1.01 ≈ ₹23,23,391. You've put in ₹12,00,000, so the estimated gain is about ₹11,23,391.

One detail people miss: dividing 12% by 12 and compounding monthly gives an effective annual return of (1.01)¹² − 1 = 12.68%, not 12%. That's how most SIP calculators, including the SIP Calculator here, treat the rate. If you want an effective 12% a year, the monthly rate should be about 0.949%. The difference is small over a few years and grows over long ones.

Time does most of the work

Doubling the period from 10 to 20 years doubles what you put in but more than quadruples the ending value. The early instalments are the ones that do the heavy lifting, because they compound the longest. This is the strongest argument for starting a SIP early, even with a small amount, and it doesn't depend on SIP versus lump sum at all.

SIP vs lump sum on the same ₹12 lakh

Now the real question. Say you have ₹12,00,000 today. Option A invests it all now. Option B invests ₹10,000 a month for 10 years. If returns are a steady 1% a month in both cases:

• The lump sum grows to 12,00,000 × (1.01)¹²⁰ ≈ ₹39,60,464.
• The SIP alone reaches about ₹23,23,391.

That looks like a rout, but it's an unfair comparison. In option B, most of the ₹12 lakh sits idle for years. Nobody would actually leave it in a savings account earning nothing. A fairer version parks the unused cash in a liquid or debt fund and moves ₹10,000 a month from there into equity, which is what a systematic transfer plan (STP) does. If the parked money earns 0.5% a month (about 6% a year), option B ends at about ₹28,59,679. Better, but still well behind the lump sum.

The reason is simple. If markets rise on average, money that's invested earlier gets more time in a rising market. Spreading the money out delays that. In a steadily rising market, lump sum wins, and the longer the spreading period, the bigger the gap.

What happens when the market falls

Returns aren't steady, so let's add a crash. Each scenario below has the market fall 30% over a single year, with 1% a month in every other month. Only the timing of the bad year changes.

Look at the lump sum column. The ending value is identical whether the crash comes first or last. That's not a coincidence. With a single investment, the final value is just the starting amount multiplied by every month's return, and multiplication doesn't care about order. Lump sum investors are exposed to the total return over the period, not to when the bad year happens.

SIP investors are different. A crash in year 1 hurts very little, because hardly any money is invested yet, and the following SIP instalments buy at low prices. In that scenario, SIP plus parked cash beats the lump sum. A crash in year 10 is the worst case for a SIP, because by then almost all the money is in the market. SIPs are sensitive to sequence; lump sums aren't.

Rupee cost averaging, with real numbers

You'll often read that SIPs lower your average cost. Here's what that means. Invest ₹6,000 in each of three months when the fund's NAV is ₹100, ₹80 and ₹120. You buy 60, 75 and 50 units, so 185 units for ₹18,000. Your average cost per unit is 18,000 ÷ 185 = ₹97.30, below the simple average NAV of ₹100. A fixed amount automatically buys more units when prices are low.

That's real, but it's not free money. It only guarantees your average cost is below the average price over the period you invested. It doesn't guarantee your cost is below what a lump sum on day one would have paid. If the NAV had gone 100, 110, 120, a lump sum at ₹100 would have done better.

So which should you pick?

• Your money arrives monthly (salary). This isn't really a choice. A SIP matches how you earn, and the lump sum comparison doesn't apply.
• You have a windfall and a long horizon. On the maths, investing sooner tends to come out ahead more often than not, because markets have tended to rise over long periods. But that's a tendency, not a promise.
• You'd panic if it fell 30% next month. Then spreading it over 6 to 12 months through an STP is a reasonable trade. You give up some expected return in exchange for less regret, and an investor who stays invested beats one who sells in a panic.
• You need the money in under three years. Equity funds, whether lump sum or SIP, can be down over that kind of period. That's a question of asset choice, not entry method.

Limitations of these numbers

• Constant returns are a simplification. The SIP calculator uses one fixed rate. Real equity returns swing year to year, which the crash table only hints at.
• The figures ignore capital gains tax, exit loads and expense ratios. An expense ratio is already reflected in a fund's published NAV, but your chosen rate should be a net-of-costs assumption.
• Many people raise their SIP each year with salary increments. The calculator doesn't model a step-up; you can approximate it by adding up separate SIP results for each block of years.
• Past returns don't set future ones. 12% is an assumption, not a forecast. Try 8% and 10% in the calculator to see how sensitive the result is.

This guide explains the arithmetic. It isn't personal investment advice, and Toolminex isn't a registered investment adviser. For decisions that depend on your tax situation and goals, talk to a SEBI-registered adviser.