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Discrete and continuous compounding conventions

Discrete compounding uses a specified period count. Continuous compounding uses an exponential factor under its own annual-rate convention.

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Hold the nominal-rate model constant

Fictional 8% annual-rate model
ConventionEffective annual growth
1 periods per year8%
2 periods per year8.16%
4 periods per year8.2432%
12 periods per year8.3%
365 periods per year8.3278%
Continuous8.3287%

Read the continuous benchmark

The discrete factors approach exp(0.08) as the frequency increases. The comparison concerns these stated mathematical factors, not an offer that credits every moment under otherwise identical product terms.

Keep rate and horizon units matched

A continuously compounded annual rate multiplies a time horizon measured in years inside the exponential. A periodic rate belongs with a count of those same periods.

Check other terms before a real comparison

Fees, taxes, risk and access can alter a realised or net return. The higher gross factor in this table does not by itself determine the better real-world choice.

Further references