Effective Annual Yield Calculator
From bond face value, annual coupon and payment frequency, compute the coupon rate and effective annual yield.
Input Data
Results
At a glance:The Effective Annual Yield (EAY) computes the coupon rate and the real compounded annual return from the bond face value, total annual coupon and payment frequency. Coupon rate = total annual coupon ÷ face value; EAY = (1 + coupon rate ÷ frequency)^frequency − 1. EAY assumes each coupon received can be reinvested at the same rate, so the more frequent the payments, the higher the EAY above the coupon rate.
Formula
Coupon rate = total annual coupon ÷ face value.
EAY = (1 + coupon rate ÷ frequency)^frequency − 1.
EAY assumes reinvestment of each coupon at the same rate, so higher frequency → EAY above coupon rate.
$$$EAY = \\left(1+\\dfrac{c}{f}\\right)^{f}-1$$$$$(5%)$\\left(1+\\frac{0.05}{2}\\right)^{2}-1\\approx5.0625\\%$$$How to Use
- Enter the bond face value and total annual coupon.
- Select the payment frequency (e.g. semi-annual).
- Get the coupon rate and effective annual yield instantly.
EAY at face HK$1,000 under different coupons and payment frequencies
| Annual coupon (HK$) | Coupon rate | Frequency | Effective annual yield (EAY) |
|---|---|---|---|
| 50 | 5% | Annual (1) | 5.0000% |
| 50 | 5% | Semi-annual (2) | 5.0625% |
| 60 | 6% | Quarterly (4) | 6.1364% |
| 80 | 8% | Monthly (12) | 8.3000% |
Case Studies
Case 1: Semi-annual EAY
Bond face HK$1,000, total annual coupon HK$50, paid semi-annually (frequency = 2). Coupon rate = 50 ÷ 1,000 = 5%.
EAY = (1 + 0.05/2)^2 − 1 = (1.025)^2 − 1 = 1.050625 − 1 ≈ 5.0625%.
Although the nominal coupon rate is 5%, because interest is paid twice a year and reinvested, the real annual return is about 5.06%, slightly above the coupon rate. That 0.06-point gap is the compounding of coupon reinvestment. The more frequent the payments, the clearer the gap.
Case 2: How frequency lifts EAY
Compare two HK$1,000 bonds: A coupon 6% paid quarterly, EAY = (1 + 0.06/4)^4 − 1 ≈ 6.1364%; B coupon 8% paid monthly, EAY = (1 + 0.08/12)^12 − 1 ≈ 8.30%. Higher coupon and more frequent payment widen the EAY-above-coupon gap.
A's EAY is about 0.14 points above coupon; B's about 0.30 points.
The higher the frequency, the earlier coupons land and reinvest, the stronger the compounding, the higher the EAY above the nominal rate. So to compare bonds with different frequencies, convert to EAY, not coupon rate. EAY only considers coupon and reinvestment, not the purchase-price/face-value gap; for a discount or premium purchase the true return is YTM, not EAY. EAY also assumes reinvestment at the same rate, which varies with the market.
FAQ
What is the difference between EAY and the coupon rate?
The coupon rate is only the nominal ratio of coupon to face value; EAY adds the compounding effect of reinvesting coupons. When paid more than once a year, EAY is higher than the coupon rate.
Is EAY the same as Yield to Maturity (YTM)?
No. EAY only considers the coupon and its reinvestment; it does not involve the price paid versus face value. YTM includes the purchase price, coupons and principal repayment at maturity.
Is more frequent payment always better?
At the same coupon rate, more frequent payment gives a slightly higher EAY because of more reinvestment chances, but the real return also depends on actually being able to reinvest at the same rate.
EAY vs YTM — which should I look at?
Both measure bond return but cover different scope. EAY (Effective Annual Yield) only considers 'coupon and its reinvestment compounding' — it converts the coupon rate by payment frequency into a real annual return, reflecting the layer of 'receive coupon, reinvest for interest'. It does NOT involve the difference between your purchase price and face value. YTM (Yield to Maturity) is broader — assuming you hold to maturity, it combines three elements: all coupons received, their reinvestment, and the key 'gap between purchase price and principal repaid (face value)' (capital gain or loss). Example: a HK$1,000 face, 5% coupon bond bought at a HK$950 discount returns the full HK$1,000 at maturity; the HK$50 gap (capital gain) is counted by YTM and lifts the real return, but EAY shows none of it. Bought at HK$1,050 premium, the HK$50 capital loss lowers YTM, and EAY again shows none. Which to use? If you care about 'the full annualised return holding to maturity', especially a bond bought at a discount or premium, use YTM because it counts the gap — that is the true return. EAY suits purely comparing 'coupon reinvestment effect across frequencies', or when the bond is bought exactly at par with no gap. Rule of thumb: EAY counts 'coupon + reinvestment'; YTM counts 'coupon + reinvestment + price gap'; the latter is closer to actual return, especially when not bought at par.
Is more frequent payment always higher return? Limits of the EAY assumption?
At the same coupon rate, more frequent payment does give a slightly higher EAY — coupons arrive earlier and reinvest sooner, stronger compounding. Example: same 6% coupon rate, paid annually EAY is 6%, paid quarterly rises to about 6.14%, paid monthly even higher. But two caveats. First and most critical: EAY assumes coupons reinvest at the same rate. The formula assumes each coupon is immediately reinvested at the same coupon rate. In reality market rates move; if rates fall when you receive coupons, you can only reinvest at a lower rate (reinvestment risk) and actual return is below EAY; if rates rise it may exceed EAY. The more frequent the payments, the bigger this assumption's effect. Second: EAY's gain diminishes and excludes the price gap. From annual to monthly the rise is noticeable, but beyond that (weekly, daily) the gain is tiny because compounding has a mathematical limit. And as noted, EAY ignores the purchase-price/face-value gap, so a premium purchase may have a real return (YTM) below EAY. So: 'frequent payment' raises EAY slightly in theory under same-rate reinvestment, but the extra return is limited and hinges on an assumption that may not hold. Don't judge a bond by frequency alone — also weigh the coupon rate itself, purchase price (discount/premium), credit risk and rate outlook, and compare with YTM. This calculator's EAY is for theoretical comparison of coupon reinvestment; assess real return with all the above.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.