How to Use This Calculator
- 1
Enter Bond Details
Input the face value, purchase price, annual coupon rate, and market/yield rate. The calculator works for both discount bonds (purchase below face) and premium bonds (purchase above face).
- 2
Set Term and Frequency
Enter years to maturity and select the payment frequency (annual, semi-annual, quarterly, or monthly). Semi-annual is standard for most bonds.
- 3
Review Return and Schedule
See total return, effective annual yield, discount/premium amount, total interest income, and annual amortization. The Insights panel shows phantom income (OID), the amortization pattern over time, and your yield advantage. The table shows the full period-by-period amortization schedule.
Example Calculation
An investor purchases a $10,000 face value bond for $9,500, with a 5% coupon rate and 6% market yield, maturing in 10 years with semi-annual payments.
Face Value
$10,000
Purchase Price
$9,500
Coupon Rate
5.0%
Market / Yield Rate
6.0%
Years to Maturity
10
Payment Frequency
Semi-Annual
Results
Total Return
$5,500
Effective Annual Yield
6.090%
Discount Bond
$500
Total Interest Income
$5,940.46
Annual Amortization
$94.05
Insights card shows $94.
Tips
Watch for Phantom Income
The Insights panel shows the difference between coupon cash received and accounting interest income. For discount bonds, you owe tax on the OID accretion each year even though you don't receive that cash until maturity.
Understand the Amortization Pattern
Under the effective-interest method, discount amortization increases each period (carrying value grows, so interest income grows while coupon stays fixed). The Insights panel shows the first and last period amounts so you can see the range.
Compare Yield to Coupon
The Insights panel quantifies the yield advantage — the 1.09% spread between the 6.09% effective yield and 5% coupon rate. This spread represents the discount accretion component of your return.
Understanding Bond Discount Amortization
The Amortized Bond Discount Calculator shows how bond discounts (or premiums) are amortized using the effective-interest method.
Enter the bond's face value, purchase price, coupon rate, market yield, maturity, and payment frequency to see total return, effective yield, and a full period-by-period amortization schedule.
The Insights panel shows the phantom income (OID) gap between coupon cash and recognized interest income, the amortization pattern across periods, and the yield advantage from the discount.
The table tracks carrying value, interest income, and amortization for every period.
The Effective-Interest Method
Each period follows four steps:
Interest Income = Carrying Value x (Market Rate / Frequency)
Coupon Payment = Face Value x (Coupon Rate / Frequency)
Amortization = Interest Income - Coupon Payment
New Carrying Value = Old Carrying Value + Amortization
For discount bonds, interest income exceeds the coupon, so amortization is positive and carrying value increases.
For premium bonds, the coupon exceeds interest income, so amortization is negative and carrying value decreases.
Worked Example: $10,000 Bond at 5% Coupon, 6% Market Yield
A $10,000 face value bond purchased for $9,500 with a 5% annual coupon, 6% market yield, 10 years to maturity, and semi-annual payments.
Setup:
- Discount: $10,000 - $9,500 = $500 (5% below face)
- Semi-annual coupon: $10,000 x (5% / 2) = $250
- Semi-annual market rate: 6% / 2 = 3%
- Total periods: 10 x 2 = 20
Period 1:
- Interest Income: $9,500 x 0.03 = $285.00
- Coupon Payment: $250.00
- Amortization: $285.00 - $250.00 = $35.00
- Closing Carrying Value: $9,500 + $35.00 = $9,535.00
Summary:
- Total Return: $5,000 coupons + $500 discount gain = $5,500
- Effective Annual Yield: (1 + 0.03)^2 - 1 = 6.090%
- Total Interest Income: $5,940.46 (accounting basis, includes OID)
- Annual Amortization: $94.05 average per year
- Phantom Income: $594.05/yr income recognized - $500/yr coupon cash = $94.05/yr taxable OID
Discount vs Premium: How Amortization Differs
| Discount Bond | Premium Bond | |
|---|---|---|
| Purchase Price | Below face value | Above face value |
| Market Rate vs Coupon | Market > Coupon | Market < Coupon |
| Amortization Direction | Positive (carrying value rises) | Negative (carrying value falls) |
| Interest Income vs Coupon | Income > Coupon | Income < Coupon |
| Tax Impact | Phantom income (OID) — taxed annually | Reduces taxable interest income |
| Amortization Trend | Increases each period | Decreases each period |
| At Maturity | Carrying value converges toward face | Carrying value converges toward face |
Tax Treatment: OID vs Market Discount
The tax treatment depends on how the discount originated:
Original Issue Discount (OID): Bonds issued below par.
The amortized discount is taxable as ordinary income each year, even though cash isn't received until maturity.
This calculator's amortization schedule shows the annual OID income to report.
Market Discount: Bonds purchased below par in the secondary market (originally issued at or near par).
Market discount is generally recognized as ordinary income only when the bond is sold or matures, unless you elect to accrue it annually.
If you elect annual accrual, the effective-interest method shown here applies.
Premium Bonds: You may elect to amortize the premium to reduce taxable interest income each year (Section 171).
If you don't elect, the full coupon is taxable and the premium becomes a capital loss at maturity.
Frequently Asked Questions
What is a bond discount?
A bond discount occurs when you buy a bond below its face value. This happens when the bond's coupon rate is lower than prevailing market rates — investors pay less to achieve a competitive yield. For a $10,000 bond purchased at $9,500, the $500 discount compensates for the below-market 5% coupon.
What is the effective-interest method?
The effective-interest method calculates interest income each period by multiplying the carrying value by the market rate. For period 1: $9,500 x 3% = $285.00 interest income vs $250.00 coupon payment. The $35.00 difference is the discount amortization, which increases the carrying value to $9,535.00. This continues until maturity.
What is phantom income (OID)?
For discount bonds, the IRS considers the amortized discount as Original Issue Discount (OID), which is taxable each year as ordinary income even though you don't receive the cash until maturity. In the default example, you receive $500/yr in coupon cash but recognize $594.05/yr in interest income — the $94.05/yr difference is phantom income you owe tax on.
Does this calculator work for premium bonds?
Yes. Enter a purchase price above face value and the calculator switches to premium amortization mode. For premium bonds, the coupon exceeds interest income, so the amortization is negative — the carrying value decreases toward face value, and premium amortization reduces your taxable interest income each period.
Why does amortization increase each period for discount bonds?
Because interest income = carrying value x market rate. As the carrying value grows (from previous periods' amortization), interest income grows too. But the coupon payment stays fixed. The widening gap between growing interest income and constant coupon means the amortization amount increases each period.