Method, example and assumptions
Model: the same total amount P is invested in both scenarios. Lump sum invests everything at month 0; DCA invests equal monthly installments C = P / (years × 12) at the start of each month. With an annual return r, the effective monthly rate is m = (1 + r/100)1/12 − 1 and n = years × 12, giving FVlump = P × (1 + m)n and FVDCA = C × (1 + m) × ((1 + m)n − 1) / m.
Worked example: P = 10,000, 10 years, 6% per year: m = 1.061/12 − 1 ≈ 0.0048676, n = 120 and FVlump = 10,000 × 1.0610 ≈ 17,908. Each installment is C = 83.33, so FVDCA = 83.33 × (1 + m) × ((1 + m)120 − 1) / m ≈ 13,605. The lump sum ends roughly 4,303 ahead — not because the strategy is better, but because every dollar is invested for the full 10 years. With a constant positive return, money invested earlier compounds longer.
The model assumes a constant annual return with no volatility. In practice, DCA is usually chosen for risk and behavior — reducing the emotional impact of price swings, or investing as money becomes available — not to raise expected return. This is not a forecast and not financial advice.
Method reviewed August 23, 2026.