About the Interest Rate Converter
Banks, lenders and textbooks quote interest in different ways: a nominal APR compounded monthly, an effective annual rate or APY, a monthly or daily periodic rate, or a continuously compounded rate. This interest rate converter takes a rate in any of those forms and shows every equivalent — so you can compare a loan quoted at 1.5% a month with one quoted at 18% APR, or a savings account’s APY with a bond’s semiannual yield.
Enter your rate, say what kind of rate it is (and how often it compounds if it is a nominal APR), then pick the compounding frequency you want to convert to. The table shows the equivalent nominal and periodic rate for every common frequency from annual to daily.
Two rates are truly equivalent when they grow money by the same amount over a year, which is what the effective annual rate measures. Note that the APR printed on US loan disclosures can also include certain fees, so it may differ from the pure interest rate converted here.
With the default inputs, the effective annual rate (apy) is 5.1162%. Change any value above to recalculate instantly.
How to use the interest rate converter
- 1Enter the interest rate you have been quoted.
- 2Choose what kind of rate it is — APR, APY, monthly, weekly, daily or continuous.
- 3If it is an APR, choose how often it compounds.
- 4Pick the compounding frequency you want to convert to.
- 5Compare the effective annual rate (APY) across offers — higher APY is better for savings, lower for loans.
Formula and method
Every rate is first converted to the effective annual rate (EAR, also called APY), which is how much one unit of money grows in a year. A nominal APR compounded m times a year becomes (1 + APR/m)^m − 1; a periodic rate p charged n times a year becomes (1 + p)^n − 1; a continuous rate r becomes e^r − 1.
From the EAR, the equivalent nominal rate for any other frequency n is n × ((1 + EAR)^(1/n) − 1), and the rate per period is that value ÷ n. The continuously compounded equivalent is the natural log of (1 + EAR). All outputs therefore describe exactly the same growth over a year.
- EAR
- Effective annual rate / APY (decimal)
- APR
- Nominal annual rate (decimal)
- m, n
- Compounding periods per year
- r_c
- Continuously compounded rate
Worked examples
5% APR compounded monthly
5% ÷ 12 = 0.41667% a month; (1.0041667)^12 − 1 gives an APY of 5.1162%. The same growth with daily compounding needs only a 4.9900% APR, and with continuous compounding 4.9896%.
6% APY to a monthly APR
A 6% effective yield is equivalent to 12 × (1.06^(1/12) − 1) = 5.8411% compounded monthly, or 0.48676% per month.
1.5% per month on a credit card or loan
1.5% a month is often quoted as 18% APR, but compounding makes the effective annual cost (1.015)^12 − 1 = 19.56%.
5% compounded continuously
e^0.05 − 1 = 5.1271% effective. The equivalent daily-compounded APR is 5.0003%.
Frequently asked questions
What is the difference between APR and APY?+
APR is the nominal yearly rate without compounding; APY (or effective annual rate) includes the effect of compounding. A 5% APR compounded monthly equals a 5.116% APY. Savings accounts advertise APY, while loans usually quote APR.
How do I convert a monthly interest rate to an annual rate?+
To get the effective annual rate, use (1 + monthly rate)^12 − 1. Multiplying by 12 gives only the nominal APR. For example, 1% a month is a 12% APR but a 12.68% effective annual rate.
What is a nominal vs effective interest rate?+
A nominal rate is the stated annual rate before compounding. The effective rate is the actual annual growth after compounding. They are equal only when interest compounds once a year.
How do I convert an annual rate to a daily rate?+
For a nominal APR, divide by 365 (some lenders use 360). For the daily rate that exactly matches an APY, use (1 + APY)^(1/365) − 1. At 5% APY that is about 0.01337% a day.
Why is continuous compounding the highest?+
Compounding more often means interest starts earning interest sooner. As the number of periods grows without limit, the effective rate approaches e^r − 1, the maximum possible for a given nominal rate.