Interest Rate Calculator
Convert nominal APR to effective annual APY yields. Generate an equivalent rate matrix across daily, weekly, monthly, and continuous compounding.
Equivalent to Nominal APR: 4.5% compounded monthly
Interest Rate Details
| Compounding Frequency | Equivalent Nominal APR | Periodic Interest Rate | Effective APY Yield | 1-Year Earnings on $10,000 |
|---|---|---|---|---|
| Annual (1/Year) | 4.5940% | 4.5940% | 4.5940% | $459 |
| Semi-Annual (2/Year) | 4.5424% | 2.2712% | 4.5940% | $459 |
| Quarterly (4/Year) | 4.5169% | 1.1292% | 4.5940% | $459 |
| Monthly (12/Year) | 4.5000% | 0.3750% | 4.5940% | $459 |
| Semi-Monthly (24/Year) | 4.4958% | 0.1873% | 4.5940% | $459 |
| Bi-Weekly (26/Year) | 4.4955% | 0.1729% | 4.5940% | $459 |
| Weekly (52/Year) | 4.4935% | 0.0864% | 4.5940% | $459 |
| Daily (365/Year) | 4.4919% | 0.0123% | 4.5940% | $459 |
| Continuous Compounding | 4.4916% | 4.4916% | 4.5940% | $459 |
How Interest Rates are Compounded
When banks or financial institutions advertise interest rates, they often present the nominal Annual Percentage Rate (APR). However, because interest compounds periodically, the actual annual yield you pay or receive is higher.
The Compounding Mathematical Formulas
To convert a nominal interest rate (APR) to the effective rate (APY), we use the following equation:
Where m is the compounding frequency (e.g. 12 for monthly, 365 for daily). To convert back from APY to APR, we rearrange:
Comparing Equivalent Nominals
If an investment pays 6% APR compounded monthly, what is the equivalent rate if it compounded daily? By standardizing to the same target APY, our calculator computes the exact equivalent nominal rate for each compounding frequency, making it easy to compare CD offers, bond yields, and mortgage options side-by-side.
Frequently Asked Questions About Interest Rates
What is the difference between APR and APY?
APR (Annual Percentage Rate) does not account for compounding interest within the year; it is simply the periodic interest rate multiplied by the number of periods in a year. APY (Annual Percentage Yield) is the actual return rate reflecting compounding interest over a full year.
How does compounding frequency impact APY?
The more frequently interest is compounded, the higher the APY. For example, a 5.0% APR compounded daily yields a 5.13% APY, whereas the same 5.0% APR compounded monthly yields a 5.12% APY.
What is continuous compounding?
Continuous compounding is the mathematical limit of compounding interest as the compounding frequency becomes infinitely large. Its equation employs the mathematical constant 'e': APY = e^r - 1.
Can this convert between APR and APY?
Yes. Convert nominal APR to effective APY under variable compounding frequencies.