Methodology

Every calculator on Caspenda shows its math. Here is exactly how the numbers are computed.

The core formula

All three calculators build on the same standard compound-interest formula. With regular contributions added at the end of each period, the balance after N periods is:

FV = P · (1+i)N + M · ( ((1+i)N − 1) / i )
  • P — initial (lump) investment
  • M — contribution per period
  • i — interest rate per period
  • N — total number of periods (years × periods per year)

If the rate is 0%, the formula reduces to FV = P + M·N (no growth).

How the per-period rate is derived

You enter a nominal annual rate (e.g. 7%) and a compounding frequency. We first convert it to an effective annual rate, then to a rate per contribution period:

Effective annual:  EA = (1 + r/f)f − 1
Rate per period:    i = (1 + EA)1/ppy − 1
  • r — nominal annual return
  • f — compounding frequency per year (1 annual, 2 semi, 4 quarterly, 12 monthly, 365 daily)
  • ppy — contribution periods per year (12 monthly, 26 biweekly, 52 weekly)

DCA vs Lump Sum

Both paths use the same total, the same period and the same return:

  • Lump Sum: the whole amount is invested in period 1 and compounds for all N periods: FV = T·(1+i)N
  • DCA: an equal amount M = T / N is invested at the end of each period: FV = M·(((1+i)N − 1)/i)

Key assumptions

  • Contributions are made at the end of each period and invested immediately.
  • Returns are nominal, pre-tax and pre-inflation.
  • The return rate is constant for the whole period — no market volatility is modeled.
  • No fees, commissions, taxes or inflation are included.
  • All results are hypothetical. They are projections of a formula, not promises of future performance.

Limitations you should know

The DCA vs Lump Sum calculator assumes a constant positive return, under which lump sum always wins mathematically. Real markets fluctuate. DCA's value is reducing the risk of bad timing, which this model does not attempt to quantify. Real outcomes will differ from any single projection.

Data & privacy

All calculations run locally in your browser. No inputs are sent to a server and no data is stored. We show nothing from external market data sources; the only "market data" you'll find is the return assumption you enter yourself.

Educational purposes only — not financial advice. Last updated: August 2026.