Comparing Compounding Frequencies at the Same Nominal Rate

For the same nominal annual rate $r\%$ and the same time $t$, more frequent compounding always gives a larger amount. This is because compounding more often means interest starts earning its own interest sooner — the interest-on-interest effect from the first section compounds more times within the same $t$ years. For the same $P$, $r$ and $t$:

with strict inequality for any genuine investment period — for the same quoted nominal rate, monthly compounding gives the highest amount and yearly compounding the lowest.

Comparing the amount, or the compound interest, under two or three different compounding frequencies for the same principal, rate and time is a common WBCHSE semester exam Compound Interest question type — see the comparison Worked Example below. …