Effective Annual Yield (EAY) Calculator

Face Value ($ F $):

Annual Coupon Payment ($ C $): USD

Coupon Frequency ($ m $):

1. What is Effective Annual Yield (EAY)?

Definition: Effective Annual Yield (EAY) is the actual annual rate of return earned on an investment, accounting for the effect of compounding interest from multiple coupon payments throughout the year.

Purpose: EAY provides investors with a way to compare bonds with different coupon payment frequencies on an equal basis.

2. How Does the EAY Calculator Work?

The calculator uses the following formulas:

\[ CR = \frac{C}{F} \times 100\% \]

\[ EAY = \left(1 + \frac{C/m}{F}\right)^m - 1 \]

Where:

$ F $: Face Value of the bond
$ C $: Total annual coupon payment
$ m $: Number of coupon payments per year
$ CR $: Coupon Rate (annual percentage)
$ EAY $: Effective Annual Yield

Steps:

Enter the Face Value of the bond and select currency
Enter the total Annual Coupon Payment in the same currency
Select the Coupon Frequency (how often payments are made)
The calculator first determines the Coupon Rate (CR)
Then calculates the periodic coupon payment (C/m)
Determines the periodic yield (periodic payment ÷ face value)
Calculates the Effective Annual Yield accounting for compounding
Results are formatted and displayed as percentages

3. Importance of EAY Calculation

Calculating EAY is essential for:

Bond Comparison: Compare bonds with different payment frequencies
Investment Decisions: Understand the true yield of fixed-income investments
Portfolio Management: Accurately assess fixed-income portfolio performance

4. Using the Calculator

Example 1: Calculate for a $1,000 bond with $50 annual coupon paid semi-annually

Face Value: $1,000
Annual Coupon: $50
Coupon Frequency: Semi-annually (2)
Coupon Rate: (50/1000)×100 = 5.00%
Periodic Payment: $50/2 = $25
Periodic Yield: $25/$1000 = 0.025
EAY: (1 + 0.025)^2 - 1 = 0.050625 or 5.0625%

Example 2: Calculate for a €5,000 bond with €300 annual coupon paid quarterly

Face Value: €5,000
Annual Coupon: €300
Coupon Frequency: Quarterly (4)
Coupon Rate: (300/5000)×100 = 6.00%
Periodic Payment: €300/4 = €75
Periodic Yield: €75/€5000 = 0.015
EAY: (1 + 0.015)^4 - 1 ≈ 0.06136 or 6.136%

5. Frequently Asked Questions (FAQ)

Q: How does EAY differ from coupon rate?
A: Coupon rate is the simple annual rate, while EAY accounts for compounding from multiple payments.

Q: Why does EAY increase with more frequent payments?
A: More frequent payments allow earlier payments to be reinvested, creating a compounding effect.

Q: Is EAY the same as APY (Annual Percentage Yield)?
A: Yes, they are conceptually similar - both measure the actual annual yield including compounding.