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How This Tool Works
Calculation Method
Reads Lump sum, Years, Annual return, DCA period and Note, then returns the result shown on this page.
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One year: $12k at 7%
What this means for your numbers: The worked example's $401 gap is 3.3% of principal over one year, the expected cost of averaging. Vanguard's historical hit rate: lump sum wins ~68% of rolling windows.
Illustrative breakdown using the worked example above. The calculator computes your own numbers with the same formula.
The arithmetic behind the two paths
The lump sum side is one compound-growth calculation: amount multiplied by (1 + rate/12) raised to the power of months. Enter $12,000, a 6% annual return, and a 10 year horizon and that is 12,000 x (1.005)^120 = $21,832.76, a gain of 81.9%. Monthly compounding is used on both sides so the comparison is like for like.
The DCA side models each slice separately. With the same inputs and a 24 month spread, the deposit is 12,000 / 24 = $500 per month. The first $500 compounds for 119 months, the second for 118, and so on down to the last slice, which compounds for 96 months (120 minus 24). Adding the 24 terms gives $20,525.40, a gain of 71.0%.
The difference is $1,307.36 in favour of the lump sum. That gap is the cost of holding money in cash during the spread window: the average DCA slice sits on the sidelines for 12 months at 6%, so it misses roughly 6% of growth on half the money, which is about what $1,307 represents over the full decade.
You can check the model's limits with the period input itself. Set the spread to 1 month and the DCA side becomes a single $12,000 deposit invested for all 120 months, which is mathematically identical to the lump sum result: both read $21,832.76 and the difference is zero. The calculator caps the spread at the horizon, so on a 6 month horizon a 12 month plan is truncated to 6 deposits rather than extending past the end date.
Where the answer flips and where it is silent
At a 0% return the two columns are always equal. With 0% typed in, the lump sum stays $12,000 and every DCA slice also sums to $12,000 no matter the spread, so the tool reports a tie. The spread window only matters because of returns, which is why the recommendation depends entirely on the rate you enter.
Negative rates reverse the winner. At -3% annual return, the same $12,000 over 10 years gives $8,886.48 for the lump sum versus $9,170.30 for the 24 month DCA plan, a $283.82 edge for spreading. Falling markets reward holding cash during the entry window, which is the whole rationale for DCA as risk control rather than return maximisation.
The boundary cases behave predictably. A period value of 1 collapses to the lump sum result, as shown above, and values larger than the horizon are clipped to the number of months available. The model has no floor at zero growth: it will happily show both columns shrinking at negative rates, which is intentional, since a real bear market does the same thing.
What the model does not capture matters as much as what it does. It assumes a constant monthly return with no volatility, so it cannot show the case where a lump sum invested just before a crash ends behind DCA even over a long horizon. It also ignores dividends paid on the uninvested cash balance, transaction costs, taxes, and inflation, none of which change the ordering between the two columns at the same rate but all of which shrink the dollar gap in real terms. Treat the output as the expected return comparison, not a guarantee about any single historical or future path.