Effective Annual Rate
What a quoted rate really costs once compounding is counted.
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Formula
How the calculation works
A quoted rate and what you actually pay are different numbers whenever interest compounds more than once a year. 12% compounded monthly is 12.68% a year, because each month's interest earns interest in the months that follow. The 0.68 point gap is the cost of compounding frequency, and it is why the effective rate is the only fair basis for comparison.
The gap grows with both the rate and the frequency. At 12% monthly it is 0.68; at 24% monthly it is about 1.36, and daily compounding at the same rate pushes it a little further. The pattern is that halving the compounding period does not halve the gap -- it shrinks quickly towards a limit, so monthly and daily are much closer to each other than annual and monthly.
This matters most for borrowing, where the gap is money leaving your account, but it applies identically to savings. Two accounts advertising 12% can pay different amounts, and two loans quoting 12% can cost different amounts, purely from the compounding schedule rather than anything in the headline.
Common mistakes
- Comparing two loans or accounts by the headline rate when the compounding schedules differ.
- Assuming the effective rate is the rate plus a fixed markup. The gap depends on both the rate and the frequency.
- Reading the quoted rate as the cost of a year. The effective rate is what a year actually costs.
When to use it
- Use the effective rate whenever you compare borrowing or savings offers, and treat the headline as advertising.
- It converts a rate for a given compounding frequency. It does not add fees or charges, which are separate from interest and often larger.
Worked example
A quoted 12% compounded monthly is really 12.68% -- 0.68 above the headline.
Common questions
Why do two places with the same rate cost different amounts?
Because the number of compounding periods differs. Monthly compounding earns interest on interest twelve times a year, annual only once. The headline can match while the real cost does not, so compare the effective rate.
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