DCA vs Lump Sum Calculator
Dollar-cost averaging spreads an investment over months while a lump sum invests it immediately, and under any positive assumed return the lump sum wins because it is exposed for longer. The case for averaging is about the range of outcomes and about behaviour, not about the expected value.
Two schedules, one amount
Defaults spread 60,000 over 12 months against investing it all on day one, at an assumed 7%.
This assumes a constant positive drift, so the lump sum wins by construction — it is exposed for longer. That is the honest limit of the comparison, and the reason the decision is not settled by this arithmetic alone.
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How the number is built
Both sides invest the same amount. They differ only in when the money is exposed, and exposure is what compounding acts on.
Lump sum = total × (1 + r)^n. Spread = (total ÷ n) × ((1 + r)^n − 1) ÷ r.
The second formula is an annuity and the first is not. Each instalment compounds only from the month it lands, so the last one earns nothing at all.
A worked example
Take the defaults: 60,000 over 12 months, against all of it on day one, at an assumed 7%.
The lump sum ends at 64,337.40.
Spread over twelve months it ends at 61,962.93.
The gap is 2,374.48 — about 4% of the amount invested, for a single year of schedule.
The reason is exposure, not returns. While averaging, your average invested balance is 32,500 of the 60,000 — a little over half. You earned the assumed return on half the money for half the period.
The comparison is rigged, and that matters
This calculator assumes a constant positive drift, so the lump sum wins by construction. Any positive rate produces the same conclusion, and a negative rate reverses it just as mechanically. The arithmetic is not discovering anything about markets; it is restating the assumption you fed it.
What the model genuinely shows is that averaging narrows the range of outcomes. Buying at twelve different prices produces something close to the average of those prices; buying once produces exactly one price, which could be the best or the worst of the twelve.
So the trade is expected value for dispersion. You give up 2,374.48 of expectation to avoid the version where the single price you paid turns out to be the year’s high.
And the price of that insurance rises steeply with the schedule. On the same 60,000 and the same assumption, spreading over 3 months costs 705.46, over 6 months 1,249.03, over 12 months 2,374.48, over 24 months 4,785.78 and over 36 months 7,425.37 — from 1.18% of the amount to 12.38%. A short schedule buys most of the behavioural benefit for a small fraction of the cost, which is the practical conclusion this page reaches.
The part the arithmetic cannot price
The strongest argument for averaging is behavioural and it is not a soft one. A plan abandoned in month three returns whatever was realised on the way out, which is usually far worse than either column here.
A single entry price is also a single thing to regret, and regret is what makes people sell. Twelve prices give nothing specific to be wrong about, which is a real advantage even though it appears nowhere in the formula.
Choose on that basis rather than on the 2,374.48. If the lump sum is the version you will hold through a 20% fall, take it. If it is the version you will not, the averaged schedule is better in the only sense that ends up mattering.
What it costs to spread
Twelve buys is twelve commissions and twelve spreads. On this site’s shared series a round trip
measures about 2% of the median bar range of 0.493, and it exceeds 10% of the bar on 15 of 576 bars.
The figures are in research/series-measurements.json.
The money waiting to be invested is not idle unless you leave it idle. Held in an interest-bearing account it earns something, which narrows the gap this page reports — the calculator assumes it earns nothing, so 2,374.48 is the widest honest version of the difference.
The original data
Of the 24,971 unique videos in research/search-study-corpus.jsonl, 53 have an instruction-shaped
title about this comparison, at a median of 9,803 views across 47 channels — and 2% are
calculator-shaped. Compound growth appears in 9 at 79,381 and index-fund investing in 26 at 88,014.
The counts come from site/rank_tools2.py, which deduplicates by video id.
Fifty-three videos at a 9,803 median is one of the weakest ratios measured here — heavily covered and lightly watched, which usually means the coverage is arguing rather than answering. The number people want is the size of the gap, and it is small.
The answer to the question on that chart is that lengthening the schedule is a market call wearing a risk-management costume. Spreading 60,000 over 24 months instead of 12 raises the gap to 4,785.78 on the same assumption, and it is only the better choice if the market falls — which is a forecast. Pick the horizon from how you will behave, and then leave it alone.
When it fails
The case that defeats most people is the one where averaging is working. Prices fall, each instalment buys more units than the last, and the schedule is doing exactly what it was chosen for — while the account shows a loss every month. That is precisely when the plan gets abandoned, and abandoning it in month five converts the strategy’s advantage into a realised loss.
The second failure is confusing this with regular saving. Investing a salary monthly is not this question — there is no lump sum to deploy.
A third is leaving the waiting money in a non-interest account. That widens the gap for no reason.
A fourth is extending the schedule after a fall. That is a forecast, not a plan.
A fifth is ignoring the transaction costs of twelve purchases.
And a sixth is treating 2,374.48 as the answer. It is the answer to an assumption.
Related
Dollar-cost averaging covers the schedule itself and where it genuinely applies. Index funds is usually what either side buys. And volatility is the quantity averaging is trading expectation against.
I would rather someone spread it over six months and stay invested than put it all in on Monday and sell in a panic on Friday. The arithmetic says one thing and the arithmetic assumes you behave. If the lump sum is the version where you check the balance every hour, then the averaged version is genuinely better, and it is better for a reason the calculator has no way to show.
— Michael Whitman
This page is educational, not financial advice. Test every idea on your own charts before risking money.