For a 6% stated annual rate compounded monthly:
(1 + 0.06/12)^12 - 1 = 0.0616778… = 6.1678…%
The effective annual rate exceeds 6% because each month's growth remains in the base for later months. At annual compounding, stated and effective annual rates are equal under this convention. At a zero rate, both are zero.
Keep the three labels separate in a workpaper: the stated annual quote, the rate applied in each period, and the effective growth over one year. Record the number of compounding intervals beside them. This small table prevents a monthly rate from being presented as an annual result or an annual quote from being applied twelve times without conversion.
EAR can align the annual compounding effect of otherwise comparable quotes. It does not automatically include fees, cash-flow timing differences, taxes, credit risk, liquidity, product options, or legal disclosure rules. Equal EARs also do not make two products identical.
Keep at least full calculator precision through the comparison and round only the displayed percentage. Early rounding of the monthly rate can materially distort a long horizon.
Put the concept to work
Understand this concept
- Explain effective annual rate as one-year compounded growth and distinguish it from the stated quote and periodic rate.
Apply this concept
- Compute an effective annual rate from a declared stated quote and frequency, then compare only alternatives with aligned horizons and included terms.
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Build on these ideas
- Compounding — Understand
To understand this concept: Required. Effective annual growth accumulates the periodic rate repeatedly.
- Effective annual rate — Understand
To apply this concept: Required. Comparison must preserve the meaning of effective annual growth.
- Stated annual rate — Understand
To understand this concept: Required. The effective rate is compared with the annual quote it transforms.
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- Effective annual rate — Apply
Required level here: understand. Required. Comparison must preserve the meaning of effective annual growth.