Effective Interest Rate Calculator
Enter your nominal (stated) interest rate and choose how often interest compounds to see the true Effective Annual Rate (EAR). The calculator also shows the periodic rate per compounding interval, the total effective rate over multiple periods, and a year-by-year balance chart so you can see how compounding frequency affects real growth. Continuous compounding is supported.
Formula
Worked example
A savings account offers 6% nominal interest compounded monthly (m = 12). Periodic rate = 6% / 12 = 0.5% per month. EAR = (1 + 0.005)^12 - 1 = 1.0616778 - 1 = 6.1678%. A $10,000 deposit held for 5 years grows to $10,000 x (1.061678)^5 = $13,488.50, earning $3,488.50 in total interest.
What is the effective interest rate?
The Effective Annual Rate (EAR), also called the Effective Annual Percentage Rate or annual equivalent rate, is the true cost or yield of a financial product once the effect of compounding is factored in. A bank that advertises 6% compounded monthly is not offering 6% growth per year: the monthly compounding means each month's interest earns interest in turn, so the actual annual growth is roughly 6.168%. The EAR is the single number that captures this reality. It lets you compare a monthly-compounding savings account against a quarterly-compounding bond on a fair footing, because both are expressed in the same annual equivalent terms.
Nominal vs. effective interest rate
The nominal rate (sometimes called the Annual Percentage Rate or APR in some jurisdictions) is the stated rate before compounding. The effective rate is what you actually earn or pay after compounding is applied. They are equal only when compounding is annual. As compounding frequency increases - from annual to monthly to daily to continuous - the gap between nominal and effective grows, though it narrows above daily because the additional gain from each extra compounding period shrinks rapidly. For a 6% nominal rate, going from annual to monthly compounding adds about 17 basis points (0.168%), while going from monthly to continuous adds only about 1.6 basis points. Understanding this distinction matters most for credit cards (which often compound daily), mortgages (commonly monthly), and savings accounts, where seemingly small differences in EAR translate into meaningful amounts on large balances over time.
How to use this calculator
Enter the stated (nominal) annual interest rate and choose a compounding frequency from the dropdown. The Effective Annual Rate updates instantly. Set the number of years to see the total effective rate over the full term and the year-by-year balance chart. If you enter a starting balance, the calculator also projects your final balance and total interest earned. The chart compares compound growth against a simple-interest baseline so you can see exactly how much compounding adds. All frequency options from annual through daily (360 or 365-day conventions) and continuous compounding are supported.
The math behind effective interest rate
For discrete compounding the formula is EAR = (1 + r / m)^m - 1, where r is the nominal rate as a decimal and m is the number of compounding periods per year. For continuous compounding, the limit as m approaches infinity gives EAR = e^r - 1, where e is Euler's number (approximately 2.71828). The periodic rate - the interest applied each compounding interval - is simply r / m. Over t years the total accumulated effective rate is (1 + EAR)^t - 1, and a principal P grows to P * (1 + EAR)^t. The Excel EFFECT(nominal_rate, npery) function applies the same discrete formula for any integer compounding frequency.
Effect of compounding frequency on a 6% nominal rate
| Compounding frequency | Periods per year | EAR (%) |
|---|---|---|
| Annually | 1 | 6.0000 |
| Semi-annually | 2 | 6.0900 |
| Quarterly | 4 | 6.1364 |
| Monthly | 12 | 6.1678 |
| Bi-weekly | 26 | 6.1800 |
| Weekly | 52 | 6.1800 |
| Daily (365) | 365 | 6.1831 |
| Continuous | infinity | 6.1837 |
All rows use a 6% stated annual rate. More frequent compounding always produces a higher EAR.
Frequently asked questions
What is the difference between EAR and APR?
These terms are used differently across countries and contexts. In the United States, APR typically refers to the nominal rate and does NOT include the effect of compounding within the year. EAR (or APY in US consumer banking) is the compounding-adjusted equivalent. In the UK and EU, APR is a broader measure that includes fees and charges as well as interest. Always check which definition applies to the product you are comparing.
Why is effective interest rate higher than the nominal rate?
Because compounding causes interest to earn interest within the year. When a bank applies interest monthly rather than annually, each month's earned interest is added to the balance, so the next month's interest is calculated on a slightly larger number. This snowball effect means the total interest over a year is higher than a simple multiplication of the monthly rate by 12. The more frequently interest compounds, the larger the gap between nominal and effective rates.
What does continuous compounding mean?
Continuous compounding is a mathematical limit where compounding happens infinitely often - not once a day or once a second, but in an infinitely small interval. The effective rate under continuous compounding is e^r - 1, where e is approximately 2.71828 and r is the nominal rate. It represents the theoretical maximum EAR for a given nominal rate. In practice, daily compounding (365 periods per year) is extremely close to the continuous limit and is used by many high-yield savings products.
How do I use EAR to compare two loans?
Convert both loans to their Effective Annual Rate and compare directly. A loan offering 5.9% compounded daily has a higher true cost than one offering 6.0% compounded annually, even though the nominal rate is lower. The EAR puts both on the same annual footing so the comparison is valid. This is exactly why lenders in many countries are required to disclose an effective or equivalent annual rate alongside the stated rate.
Is a higher EAR always bad?
Not always. A higher EAR is bad when you are the borrower (you pay more interest). It is good when you are the investor or saver (you earn more). The same calculation applies to both; the sign of the outcome is the only thing that differs. When shopping for a savings account, choose the highest EAR. When comparing loans, choose the lowest EAR.
What is the periodic rate and why does it matter?
The periodic rate is the interest rate applied at each compounding interval: the nominal rate divided by the number of compounding periods per year. For a 12% annual rate compounded monthly, the periodic rate is 12% / 12 = 1% per month. This is the rate used by lenders to calculate your monthly interest charge. Knowing the periodic rate lets you verify statements and understand exactly how much interest accrues in any single period.