Effective Annual Rate (EAR)
%
Effective Annual Rate (EAR), also called Annual Equivalent Rate (AER), is the actual annual interest rate accounting for compounding within the year. It allows comparison of loans or investments with different compounding frequencies.
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Tip: When comparing savings accounts, look for the APY (= EAR), not the APR. Banks are required to disclose APY for deposits by the Truth in Savings Act.
- 1EAR = (1 + r/n)^n − 1
- 2r = nominal (stated) annual rate, n = compounding periods per year
- 3Daily compounding always gives a higher EAR than monthly, which is higher than annual
- 4APY (Annual Percentage Yield) on savings accounts IS the EAR
12% nominal, monthly compounding=EAR = 12.68%(1 + 0.12/12)^12 − 1
12% nominal, daily compounding=EAR = 12.75%(1 + 0.12/365)^365 − 1
| Compounding | EAR | Extra interest on $10,000 |
|---|---|---|
| Annual | 12.00% | $1,200 |
| Quarterly | 12.55% | $1,255 |
| Monthly | 12.68% | $1,268 |
| Daily | 12.75% | $1,275 |
| Continuous | 12.75% | $1,275 |
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Fun Fact
Continuous compounding — where n approaches infinity — is described by the formula EAR = e^r − 1. At 12% nominal, this gives 12.7497% EAR — almost identical to daily compounding.
References
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