How to use it
- Choose whether the rate you have is a nominal yearly rate or an effective yearly rate.
- Type the rate as a percentage, for example 4.65 for 4.65%.
- Choose how often the interest is added: monthly, daily, continuously and so on.
- Read the effective yearly rate first, then the nominal and monthly rates, and the steps under the result.
How the effective rate is calculated
A nominal yearly rate is added to the balance several times a year, and each addition earns interest on the interest before it. The effective yearly rate is what one year of that growth adds up to, so it is the figure to compare when two offers add interest at different times.
With the interest added m times a year, the effective yearly rate is (1 + r ÷ m)^m − 1, where r is the nominal yearly rate. Wikipedia's page on the annual percentage yield gives the same formula, APY = (1 + i_nom ÷ N)^N − 1, and for a large number of periods e^i − 1.
EAR = (1 + r ÷ m)^m − 1
EAR effective yearly rate (APY)
r nominal yearly rate
m times the interest is added in a year- Monthly: m = 12. Quarterly: m = 4. Daily: m = 365. Once a year: m = 1.
- Continuously: EAR = e^r − 1, the limit as m grows without bound.
The monthly rate
The effective monthly rate is the growth of one month: (1 + EAR)^(1 ÷ 12) − 1. Added twelve times in a row, it gives the effective yearly rate.
The nominal monthly rate is the nominal yearly rate divided by twelve. Some offers quote a monthly rate and multiply it by twelve to get the yearly figure, so check which rate the contract means.
What this calculator does not include
- Fees, charges and taxes, which change the cost of a loan and the net return of a deposit.
- The bank's own rounding of rates and interest, which can differ from this exact calculation.
- Changes of the rate during the year.
Worked example: 4.65% a year, added monthly
The nominal yearly rate is 4.65%, added twelve times a year, so each month earns 4.65% ÷ 12 = 0.3875%.
The effective yearly rate is (1 + 4.65% ÷ 12)^12 − 1 = 4.7504%, which is 4.75% to two decimals. A deposit of 100 earns about 4.75 in a year.
| Figure | Value |
|---|---|
| Effective yearly rate (APY) | 4.7504% |
| Nominal monthly rate | 0.3875% |
| Effective monthly rate | 0.3875% |
Frequently asked questions
What is the difference between APR and APY?
The APR is the nominal yearly rate, before the compounding. The APY, or effective yearly rate, includes the interest added during the year, so it is the same as the APR when interest is added once a year and higher than it otherwise.
Why do banks quote the APY on deposits and the APR on loans?
Banks often quote the APY on deposits, where it shows the higher return the customer receives, and the APR on loans, which is the rate the borrower pays. Wikipedia's page on the annual percentage yield notes the same pattern.
Does adding interest daily make much difference?
Only a little once it is added daily. At 5% a year, daily compounding gives 5.1267% and continuous compounding 5.1271%, so moving from daily to continuous adds very little.
How do I get the monthly rate from a yearly rate?
Divide the nominal yearly rate by twelve for the nominal monthly rate. For the effective monthly rate, take the twelfth root of one plus the effective yearly rate, and subtract one.
Does this calculator include fees and taxes?
No. It converts the interest rate only. Fees, charges and taxes change the real cost of a loan or the net return of a deposit, so they must be added separately.
Are the rates I enter sent to a server?
No. The calculation runs in your browser, and nothing you enter is sent to us.
Sources
- Wikipedia: Annual percentage yield (the APY formula and the 4.65% example)
- Wikipedia: Annual percentage rate (the effective annual rate and the rate format)
Figures and text last checked on Tuesday, November 10, 2026.