Bond Amortization and Yield Accretion

An investor buys a bond at $1,050 that will repay only $1,000 at maturity. If the accountant just recorded the $60 annual coupon as income every year and ignored the $50 that's guaranteed to evaporate, the books would overstate the bond's true return for years — right up until maturity, when a sudden $50 loss would appear from nowhere. Amortization spreads that built-in loss (or gain, for a discount bond) evenly across the bond's life instead of dumping it all at the end.

The mechanics

The effective-interest method is the standard approach. Each period, recognized interest income is the bond's current book value multiplied by the yield to maturity at purchase — not the coupon rate. The difference between that recognized income and the actual cash coupon received is the amortization (or accretion) adjustment to book value.

$$\text{Interest income}_t = BV_{t-1} \times y$$ $$BV_t = BV_{t-1} + \left(\text{Interest income}_t - C\right)$$

In words: income each period is last period's book value times the locked-in yield; book value then moves by however much that income differs from the actual coupon paid. For a premium bond, income is always less than the coupon, so book value shrinks each period. For a discount bond, income exceeds the coupon, so book value grows.

Worked example

A 3-year bond, $1,000 face, 6% annual coupon ($60/yr), bought at $1,050 to yield 4.00%.

1. Year 1 income: $1050 \times 0.04 = 42.00$. Amortization: $42.00 - 60 = -18.00$. New book value: $1050 - 18.00 = 1032.00$.
2. Year 2 income: $1032.00 \times 0.04 = 41.28$. Amortization: $41.28 - 60 = -18.72$. New book value: $1032.00 - 18.72 = 1013.28$.
3. Year 3 income: $1013.28 \times 0.04 = 40.53$. Amortization: $40.53 - 60 = -19.47$. New book value: $1013.28 - 19.47 \approx 993.8$.

The small remaining gap from exact par ($1,000) is a rounding artifact of using an approximate yield; solved precisely, book value lands exactly at $1,000 the moment the final coupon and principal are paid — confirming the amortization schedule was built correctly around the true yield to maturity.

What this means in practice

Amortized cost accounting is how banks, insurers, and buy-and-hold bond funds report income on securities they don't mark to market — it produces a smoothly declining (or rising) book value and a steady recognized yield, instead of letting reported income swing with the coupon alone. It also matters for tax treatment: bond premium amortization and original-issue-discount accretion are both explicitly governed by tax rules in most jurisdictions, because otherwise investors could defer or accelerate taxable income simply by choosing which bonds to buy at a premium versus discount.