How to Use This Calculator
- 1
Enter Bond Details
Input the face value, purchase price, annual coupon rate, and market/yield rate. The purchase price must exceed face value for a premium bond.
- 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 Premium and Schedule
See the bond premium, effective annual yield, total premium amortized, total interest income, and annual amortization. The Insights panel shows the coupon breakdown (income vs return of premium), tax benefit of amortization, and yield drag. The chart and table show the full period-by-period schedule.
Example Calculation
An investor buys a $10,000 face value bond for $10,500, with a 6% coupon rate and 5% market yield, maturing in 10 years with semi-annual payments.
Face Value
$10,000
Purchase Price
$10,500
Coupon Rate
6.0%
Market (Yield) Rate
5.0%
Years to Maturity
10
Payment Frequency
Semi-Annual
Results
Bond Purchase Premium
$500
Effective Annual Yield
5.062%
Total Premium Amortized
$957.92
Total Interest Income
$5,042.08
Annual Premium Amortization
$95.79
Insights card shows period 1 coupon splits $262.
Tips
Understand the Coupon Split
The Insights panel shows how each coupon payment splits between true interest income and return of premium. In period 1, only $262.50 of the $300.00 coupon is income — the $37.50 remainder reduces your carrying value.
Evaluate the Section 171 Election
The Insights panel shows the tax benefit: electing to amortize reduces taxable interest from $600/yr (full coupon) to $504.21/yr (effective income). Without the election, you pay tax on the full coupon and take a capital loss at maturity.
Watch the Yield Drag
The Insights panel quantifies the yield drag — the 6% coupon delivers $600/yr in cash, but the effective 5.06% yield means only ~$504/yr is true income. The ~$96/yr difference is premium being returned, not earned.
Understanding Bond Premium Amortization
The Amortized Bond Premium Calculator shows how the premium on bonds purchased above face value is amortized using the effective-interest method.
Enter the bond's face value, purchase price, coupon rate, market yield, maturity, and payment frequency to see the premium amount, effective yield, and a full period-by-period amortization schedule.
The Insights panel shows how each coupon payment splits between true income and return of premium, the tax benefit of amortization under Section 171, and the yield drag from the premium.
The chart and table track carrying value and cumulative amortization over the bond's life.
The Effective-Interest Method for Premium Bonds
Each period follows four steps:
Interest Income = Carrying Value x (Market Rate / Frequency)
Coupon Payment = Face Value x (Coupon Rate / Frequency)
Premium Amortization = Coupon Payment - Interest Income
New Carrying Value = Old Carrying Value - Premium Amortization
For premium bonds, the coupon exceeds interest income, so premium amortization is positive and the carrying value declines toward face value each period.
The amortization amount increases over time because the declining carrying value produces less interest income while the coupon stays constant.
Worked Example: $10,000 Bond at 6% Coupon, 5% Market Yield
A $10,000 face value bond purchased for $10,500 with a 6% annual coupon, 5% market yield, 10 years to maturity, and semi-annual payments.
Setup:
- Premium: $10,500 - $10,000 = $500 (5% above face)
- Semi-annual coupon: $10,000 x (6% / 2) = $300
- Semi-annual market rate: 5% / 2 = 2.5%
- Total periods: 10 x 2 = 20
Period 1:
- Interest Income: $10,500 x 0.025 = $262.50
- Coupon Payment: $300.00
- Premium Amortized: $300.00 - $262.50 = $37.50
- Closing Carrying Value: $10,500 - $37.50 = $10,462.50
Summary:
- Effective Annual Yield: (1 + 0.025)^2 - 1 = 5.062% (vs 6% coupon)
- Total Interest Income: $5,042.08 (effective-interest basis)
- Total Premium Amortized: $957.92 over 20 periods
- Annual Premium Amortization: $95.79 average per year
- Yield Drag: 6% coupon - 5.06% effective = 0.94% annual drag from premium
Tax Treatment: The Section 171 Election
For taxable premium bonds, IRS Section 171 lets you elect to amortize the premium to reduce taxable interest income:
| With Election | Without Election | |
|---|---|---|
| Annual taxable interest | ~$504/yr (effective income) | $600/yr (full coupon) |
| Annual tax reduction | ~$96/yr less taxable income | None |
| At maturity | Adjusted basis = face value | Capital loss of $500 |
| Best for | Reducing annual tax liability | Deferring to capital loss treatment |
The election applies to all taxable bonds you own and is irrevocable for that year.
For tax-exempt bonds, premium amortization is mandatory — you must reduce the bond's basis but cannot deduct the amortized premium.
How Premium Size Affects the Schedule
Larger premiums create more yield drag and larger amortization amounts.
Here's how the schedule changes with different purchase prices ($10,000 face, 6% coupon, 5% market, 10 years, semi-annual):
| Purchase Price | Premium | Eff Yield | Period 1 Income | Period 1 Amort |
|---|---|---|---|---|
| $10,250 | $250 | 5.062% | $256.25 | $43.75 |
| $10,500 | $500 | 5.062% | $262.50 | $37.50 |
| $10,750 | $750 | 5.062% | $268.75 | $31.25 |
| $11,000 | $1,000 | 5.062% | $275.00 | $25.00 |
The effective yield stays the same (it's derived from the market rate, not the premium).
Notice that higher purchase prices produce less amortization per period — the higher carrying value generates more interest income, narrowing the gap between coupon and income.
A larger premium takes longer to amortize.
Frequently Asked Questions
What is a bond premium?
A bond premium occurs when you pay more than face value for a bond. This happens when the bond's coupon rate exceeds prevailing market rates — the higher coupon makes the bond worth more than par. For a $10,000 bond purchased at $10,500, the $500 premium reflects the value of receiving a 6% coupon when the market only yields 5%.
How does the effective-interest method work for premiums?
Each period: Interest Income = Carrying Value x Market Rate per period. Premium Amortized = Coupon Payment - Interest Income. New Carrying Value = Old Carrying Value - Premium Amortized. For period 1: $10,500 x 2.5% = $262.50 income, $300 - $262.50 = $37.50 amortized, carrying value drops to $10,462.50.
Should I elect to amortize the premium for taxes?
Under Section 171, you can elect to amortize the premium to reduce taxable interest income each year. In the default example, this reduces taxable interest from $600/yr to ~$504/yr. Without the election, you report the full $600 coupon as income and take the $500 premium as a capital loss at maturity. The election is generally beneficial if you want to lower annual tax liability.
Why does premium amortization increase each period?
Because interest income = carrying value x market rate. As the carrying value declines each period, interest income decreases. But the coupon stays fixed at $300. The widening gap between the fixed coupon and declining interest income means more premium is amortized each period ($37.50 in period 1, growing over time).
What's the difference between coupon cash and effective income?
Coupon cash is what you actually receive — $600/yr for a 6% coupon on $10,000 face value. Effective income is the true economic return based on what you paid — $504.21/yr at the 5.06% effective yield on $10,500. The $95.79/yr difference is return of premium, not income. The amortization schedule shows this split for every period.