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.