What a rate becomes once it compounds
Banks advertise a nominal rate, but interest is credited monthly, quarterly or daily. Each credit starts earning interest itself, so the amount you actually receive over a year exceeds the advertised figure. The annual percentage yield is that real figure.
The formula
Here n is how many times a year interest is credited. It is the only variable that separates two accounts advertising the same rate.
Worked example: 6% nominal, compounded monthly
- Monthly rate: 6 ÷ 12 = 0.5%
- APY: (1.005)12 − 1 = 6.17%
- Difference: 0.17 percentage points
On a $50,000 balance that is $85 a year of interest that the advertised rate never mentions.
How far compounding frequency can take it
| Credited | n | APY on 6% |
|---|---|---|
| Annually | 1 | 6.000% |
| Semi-annually | 2 | 6.090% |
| Quarterly | 4 | 6.136% |
| Monthly | 12 | 6.168% |
| Daily | 365 | 6.183% |
| Continuously | ∞ | 6.184% |
Notice the ceiling. Moving from annual to monthly buys 0.17 points; moving from monthly to daily buys 0.015. Beyond monthly, compounding frequency stops mattering, which is why "compounded daily" in an advertisement is worth less than it sounds.
The gap widens with the rate
At 6% the gap is 0.17 points. At 18% — a typical credit card rate — monthly compounding turns it into 19.56%, a gap of 1.56 points. Compounding works against you at exactly the rates where it hurts most.
What this calculator leaves out
Tax on the interest, monthly account fees, and any promotional rate that reverts after an introductory period. Compare the APY after fees, not before.
Reading a savings advertisement
Two accounts, one advertising 6.10% APY and one advertising 6.00% nominal compounded daily. The second is 6.18% APY and wins, despite the smaller headline number.
This is exactly why the APY figure is regulated in most markets: it is the only number that permits a direct comparison. When a rate is quoted without saying whether it is nominal or APY, assume nominal and convert it yourself before deciding.
Where the extra interest actually comes from
On a $50,000 balance at 6%, annual compounding pays $3,000. Monthly compounding pays $3,084. The extra $84 is interest earned by interest that was credited earlier in the same year.
January's $250 of interest sits in the account for eleven months and earns about $13 itself. February's earns for ten months, and so on. Add up those twelve small amounts and you have the difference between 6.00% and 6.17%.
That is the whole mechanism, and it is why the effect grows with both the rate and the balance while barely responding to compounding more often than monthly.
APY on an account you are still paying into
The yield describes the rate, not the outcome. If you add money monthly, the balance at the end is not the opening sum grown by 6.17%, because each deposit compounds only for the months remaining after it arrives.
A $10,000 opening balance plus $200 a month at 6% monthly compounding reaches about $13,240 after two years. The APY is still 6.17%; the effective return on everything you paid in is lower, because the average dollar was invested for roughly half the period.
Compare accounts on APY. Project balances with a compound interest calculator that accepts contributions.
Related calculators
- Effective interest rate calculator — the same conversion applied to borrowing
- APR calculator — the comparable figure once fees are folded in
- Compound interest calculator — what the balance actually reaches