Interest Calculator · Practical guide
Effective Annual Rate of 5% Compounded Monthly
A 5% nominal rate compounded monthly really earns 5.1162% per year — here's why.
At a glance
The Answer: 5.1162%
A nominal annual rate of 5% compounded monthly produces an effective annual rate (EAR) of 5.1162%. The formula is EAR = (1 + 0.05/12)^12 − 1. Each month your balance grows by 5%/12 = 0.4167%, and because each month's interest itself earns interest in later months, the true annual yield ends up slightly above the quoted 5%.
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Results
5% at Every Compounding Frequency
| Compounding | Effective Annual Rate | $10,000 After 1 Year |
|---|---|---|
| Simple / annually | 5.0000% | $10,500.00 |
| Monthly | 5.1162% | $10,511.62 |
| Daily | 5.1267% | $10,512.67 |
Why EAR Is the Number to Compare
Banks advertise a nominal rate or an APY, but only one of them tells you what you actually earn. APY is simply another name for the effective annual rate, so a 5% nominal rate compounded monthly is the same as a 5.1162% APY. When comparing accounts, always match APY to APY — a 5.10% APY account beats a 5% nominal monthly account even though 5.10 looks close to 5.00.
The Gap Widens at Higher Rates
Compounding effects scale with the rate: 6% compounded daily has an EAR of 6.1831%, a gap of 0.18 points, while at 5% the daily-compounding gap is only about 0.13 points. The calculator above shows the effective annual rate for any rate and frequency you enter, so you can convert any quoted rate into its true annual yield instantly.
Frequently Asked Questions
Is EAR the same as APY?
For deposit accounts, yes. APY is the effective annual rate a bank pays after compounding. On loans, the equivalent figure is sometimes called the effective rate, while APR is a different measure that includes fees.
Why is the effective rate higher than the nominal rate?
Because interest is credited during the year and immediately starts earning interest itself. Twelve monthly credits of 0.4167% multiply to more than one annual credit of 5%.
Does continuous compounding earn much more than daily?
Barely. Continuous compounding at 5% gives an EAR of about 5.1271%, versus 5.1267% daily — a difference of less than a dollar a year on $10,000.
How do I convert an APY back to a nominal monthly rate?
Take the twelfth root of (1 + APY), subtract 1, and multiply by 12. For a 5.1162% APY, that gives back the 5% nominal rate compounded monthly.