Effective Annual Yield Calculator
Enter a bond's face value and annual coupon payment to find its effective annual yield, or switch to Rate mode to convert any nominal interest rate to its effective annual equivalent. All standard compounding frequencies are supported, including continuous compounding. Results update instantly and a step-by-step breakdown shows exactly how each number is derived.
What is effective annual yield?
Effective annual yield (EAY), also called effective annual rate (EAR), is the actual return earned on an investment over one year after accounting for the compounding of interest within that year. A bond that pays coupons semi-annually, for example, lets you reinvest the first coupon payment for half a year before maturity, so the true annual return is slightly higher than the stated coupon rate. EAY makes that extra return visible, allowing direct comparisons between bonds or savings products with different payment frequencies.
The EAY formula and how it works
For a bond or any investment that pays a periodic rate r and compounds m times per year, the formula is: EAY = (1 + r / m)^m - 1. In bond mode, r is the coupon rate (annual coupon / face value) and m is the coupon frequency. In rate mode, r is the stated nominal rate and m is the chosen compounding frequency. For continuous compounding, the formula simplifies to EAY = e^r - 1, where e is Euler's number (~2.71828). The periodic rate is r / m, the fraction of the nominal rate that applies to each individual period.
Bond mode vs. rate mode - which should you use?
Use bond mode when you have a specific bond and want to find its true annual return: enter the face value, the total annual coupon in dollars, and how often coupons are paid. The calculator derives the coupon rate for you and shows the EAY. Use rate mode when you are comparing savings accounts, mortgages, or other financial products where the lender quotes a nominal annual percentage rate (APR) and a compounding schedule. By converting both products to their effective annual yields, you can compare them on equal footing regardless of their payment schedules.
Why compounding frequency matters
At a 6% nominal rate, annual compounding gives exactly 6.00% EAY. Semi-annual compounding gives 6.09%. Monthly compounding gives 6.17%. Daily compounding gives 6.18%. Continuous compounding gives 6.18% (the mathematical ceiling). The differences look small in isolation, but they compound over time: on a $100,000 portfolio held for 20 years, the difference between annual and monthly compounding at 6% nominal is roughly $5,000. When lenders advertise an APR and compound monthly, the effective cost to the borrower is higher than the headline rate. When savers see an APY, that is the EAY already, so no conversion is needed.
EAY by compounding frequency at a 6% nominal rate
| Compounding frequency | Periods per year | EAY |
|---|---|---|
| Annual | 1 | 6.0000% |
| Semi-annual | 2 | 6.0900% |
| Quarterly | 4 | 6.1364% |
| Monthly | 12 | 6.1678% |
| Weekly | 52 | 6.1800% |
| Daily | 365 | 6.1831% |
| Continuous | infinity | 6.1837% |
How the effective annual yield rises as compounding becomes more frequent, for a 6.00% nominal rate.
Frequently asked questions
What is the difference between effective annual yield and APY?
They are the same thing stated by different industries. Banks and savings products use the term APY (annual percentage yield), while bond markets use effective annual yield (EAY). Both equal (1 + r/m)^m - 1 and represent the real annual return including compounding. When you see an APY, no conversion is needed - it is already the effective figure. When you see an APR or a coupon rate, you must apply the EAY formula to find the true annual return.
How is EAY different from the coupon rate on a bond?
The coupon rate is simply the annual coupon divided by the face value - it ignores compounding. EAY is always higher than the coupon rate (unless payments are made annually, in which case they are equal), because reinvesting each coupon payment for the remainder of the year earns additional interest. For a bond paying 5% annually but distributing coupons semi-annually, the EAY is about 5.06%, not 5.00%.
What does continuous compounding mean?
Continuous compounding is the mathematical limit where interest is added at every instant rather than at fixed intervals. The formula becomes EAY = e^r - 1, where e is approximately 2.71828 and r is the nominal rate. No real product compounds truly continuously, but the concept is used in derivatives pricing and theoretical finance. In practice, daily compounding gets extremely close to the continuous limit.
Can the effective annual yield be lower than the nominal rate?
No. With compounding, EAY is always greater than or equal to the nominal rate. The only case where they are equal is when compounding happens exactly once per year (annual frequency). As soon as compounding happens more than once per year, interest earned in early periods itself earns interest in later periods, pushing the effective rate above the nominal one.
How do I compare two bonds with different coupon frequencies?
Convert each bond to its EAY using this calculator, then compare the two EAY figures directly. For example, Bond A pays 5% annually (EAY = 5.00%) and Bond B pays 4.95% semi-annually (EAY = 4.986% + compounding = approx. 5.01%). Despite the lower stated rate, Bond B has the higher effective return. EAY is the only fair comparison point when payment frequencies differ.
What is a basis point and why is the compounding gain measured in basis points?
One basis point is one hundredth of one percent (0.01%). Financial professionals use basis points to describe small differences in interest rates clearly. The gain from compounding is typically a few basis points to a few tens of basis points - small enough that percentages would look like rounding errors, but meaningful on large sums. The calculator reports the compounding gain in basis points so you can see the exact improvement over the nominal rate.