Effective Interest Rate Calculator
Calculate the effective annual interest rate (EAR/APY) from nominal rates and compounding frequency. See the true annual cost of loans or real return on investments.
Use the EFFECT() function to calculate the effective interest rate in Excel or Google Sheets:
EFFECT(nominal_rate, npery)- • nominal_rate = Nominal annual interest rate (7%)
- • npery = Number of compounding periods per year (12)
Effective Interest Rate per Period
- • i = Effective interest rate
- • r = Nominal rate (decimal: R/100)
- • m = Compounding periods per year
Effective Rate for t Periods
- • it = Total effective rate for t periods
- • t = Number of periods (years)
- • Also: it = (1 + r/m)mt − 1
Continuous Compounding
When compounding frequency approaches infinity, we use Euler's number (e ≈ 2.71828). This represents the theoretical maximum effective rate for a given nominal rate.
Common Examples
| Nominal Rate | Compounding | Effective Rate | 5-Year Return |
|---|---|---|---|
| 7% | Monthly | 7.2290% | 41.76% |
| 12% | Monthly | 12.6825% | 81.67% |
| 12% | Quarterly | 12.5509% | 80.61% |
| 12% | Daily | 12.7475% | 82.19% |
| 24% | Monthly | 26.8242% | 228.10% |
Nominal vs. Effective: The Real Cost of Money
Banks often advertise the Nominal Interest Rate to make loans look cheaper or savings look smaller than they are. The Effective Interest Rate reveals the truth by accounting for the power of compounding. Learn more with our Compound Interest Calculator.
Why the Difference Matters
The more frequently interest is compounded, the higher the effective rate becomes compared to the nominal rate. This difference might look small on a percentage basis, but over time and large sums, it compounds into significant wealth—or debt.
For Savers (APY)
You want the Effective Rate. A 5% nominal rate compounded daily yields 5.13% APY. That's "free" money just from the math of frequency.
For Borrowers (APR)
You want to watch the Effective Rate. Credit cards compounding daily turn a 20% nominal rate into an effective 22.13% annual burden.
Compounding Frequency Impact Table
Assuming a 10% Nominal Annual Interest Rate:
| Frequency | Compounds/Year | Effective Rate |
|---|---|---|
| Annually | 1 | 10.00% |
| Semi-Annually | 2 | 10.25% |
| Quarterly | 4 | 10.38% |
| Monthly | 12 | 10.47% |
| Daily | 365 | 10.52% |
Frequently Asked Questions
What is the difference between nominal and effective interest rate?
The nominal interest rate (also called stated rate) is the annual rate quoted by banks and lenders, without accounting for compounding within the year. The effective interest rate (EIR), also known as Annual Percentage Yield (APY), reflects the actual annual rate after considering how often interest is compounded. The effective rate is always higher than or equal to the nominal rate.
What is the effective interest rate of 7% compounded monthly?
Using the formula EIR = (1 + 0.07/12)12 − 1, a 7% nominal rate compounded monthly results in an effective annual rate of approximately 7.23%. Over 5 years, this compounds to a total return of 41.76%.
How do I use the EFFECT() function in Excel?
In Excel or Google Sheets, use EFFECT(nominal_rate, npery) where nominal_rate is the stated annual rate (e.g., 7%) and npery is the number of compounding periods per year.
How is APY different from APR?
APR (Annual Percentage Rate) is similar to the nominal rate and doesn't account for compounding. APY (Annual Percentage Yield), also called EAR (Effective Annual Rate), does include the effect of compounding. For savings accounts, banks typically advertise APY; for loans, they show APR.
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