APY is APR after compounding
APR is the stated yearly rate. APY is what you really earn once the interest you have already been paid starts earning interest itself. The more often it compounds during the year, the more that stacks, so APY is always at least as high as APR and higher whenever compounding beats once a year.
r is the APR as a decimal (5% is 0.05) and n is the number of compounding periods per year: 365 daily, 12 monthly, 4 quarterly, 1 annually.
Same 5% APR, different compounding
| Compounding | n | APY on 5% APR | Earned on $10,000 |
|---|---|---|---|
| Annually | 1 | 5.000% | $500 |
| Semi-annually | 2 | 5.063% | $506 |
| Quarterly | 4 | 5.095% | $509 |
| Monthly | 12 | 5.116% | $512 |
| Daily | 365 | 5.127% | $513 |
The gap between APR and APY widens as the rate rises: it is a few cents at 0.5% APR but around $52 per $10,000 at 10% APR.
The trap: comparing accounts on the wrong number
- Compare APY, not APR. APY already folds in the compounding, so it is the one figure that lets you rank two accounts fairly. A higher APR can lose to a lower one that compounds more often.
- Banks must publish APY. In the US the Truth in Savings Act requires savings, money-market and CD accounts to disclose APY, so it is the number to look for on the offer.
- APR = APY only once a year. If an account compounds annually the two match. Any faster and treating them as equal understates what you earn.
Common questions
What is the difference between APR and APY?
APR is the plain yearly rate before compounding. APY is the rate you actually earn once interest starts earning interest during the year. Whenever interest compounds more often than once a year, APY is higher than APR.
Is 5% APR the same as 5% APY?
No. At 5% APR compounded daily the APY is 5.13%, which is about $13 more per year on $10,000. They are only equal when interest compounds once a year.
How do I calculate APY from APR?
Use APY = (1 + r/n)^n minus 1, where r is the APR as a decimal and n is how many times a year it compounds (365 daily, 12 monthly, 4 quarterly, 1 annually). Multiply the result by 100 for a percentage.
