The best replacement for continuous compounding is daily compounding.

The best alternatives to continuous compounding are rated as following:
★★★★★  daily compounding
★★★  discrete
★★  annual
★★  annual compounding
★  discrete compounding
★  monthly compounding
★  compounding

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Speaking about continuous compounding, one probably shouldn't forget about annuity.

Other search terms related to continuous compounding and their ratings are:
★★★★★ annuity
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Google Trends

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continuous compounding
daily compounding
discrete