Compounding vs. Payment Frequency

Most calculators bundle "compounding" and "payment" into one frequency selector. That's a shortcut that fails the moment a real product describes interest one way and instalments another — a bond accrues semi-annually but pays quarterly; a loan compounds daily but bills monthly.

Two distinct rates

Compounding frequency — how often the bank converts a fraction of a year's interest into principal.
Payment frequency — how often cash actually changes hands.

When the two match, the calculator uses the simple periodic rate r/m. When they differ, the calculator first builds the Effective Annual Rate (EAR) and then converts back down to a per-payment rate:

$\text{EAR} = \left(1 + \frac{r}{m_{\text{comp}}}\right)^{m_{\text{comp}}} - 1, \qquad r_{\text{pay}} = (1 + \text{EAR})^{1/m_{\text{pay}}} - 1$

Without that step, every annuity factor is wrong by a few basis points — small per period, large over a 25-year horizon.

Continuous compounding

Picking "Continuous" disables the payment input: $e^{rt}$ describes a frictionless accumulation, not discrete cash events. Use it for bond pricing, option models, and academic problems; for practical loans and savings the discrete frequencies are what banks actually use.

When in doubt

Set both frequencies to the same value. The result is the textbook annuity formula. Only deviate when the product genuinely behaves that way — and document the choice next to the result.