CFA Level I Exam · Topics in Long-Term Liabilities and Equity

Effective Interest Rate Method and Bond Amortization

Updated 7 October 2026 · Fact-checked

The effective interest method sets bond interest expense each period equal to the opening carrying value multiplied by the market yield at issuance. Amortization is the gap between that expense and the cash coupon. Carrying value moves toward face value by that amount. Straight-line spreads the discount or premium evenly instead.

Understand Effective Interest Rate Method and Amortization

A bond is issued at a price set by the market yield on the issue date. If the coupon rate is below that yield, the bond sells at a discount. If the coupon rate is above it, the bond sells at a premium. The issuer records a liability at the issue price, not at face value.

That liability must end at face value on maturity. So the discount or premium has to be written off over the bond's life. This is amortization. The cash coupon is fixed. The accounting interest expense is not.

Under the effective interest method, interest expense = opening carrying value × the market rate at issuance. This is the true cost of borrowing on the amount actually owed. For a discount bond, the carrying value rises each period, so interest expense rises. For a premium bond, the carrying value falls, so interest expense falls. The difference between expense and coupon is the amortization.

Under straight-line, the total discount or premium is divided equally across all periods. Interest expense is then constant. It ignores the changing balance owed. Under IFRS, bonds measured at amortised cost use the effective interest method. Straight-line is mainly a US GAAP shortcut, allowed only when the result is not materially different.

The total interest expense over the life is the same either way: total coupons plus the discount, or total coupons minus the premium. Only the timing differs. The cash flows never change.

Key formulas to remember

Interest expense (effective interest): Interest expense = Opening carrying value × market yield per period; Use the market rate at issuance, not the coupon rate. Halve the annual rate for semiannual bonds.
Coupon paid: Coupon = Face value × coupon rate per period; This is the cash paid. It stays constant.
Discount amortization: Amortization = Interest expense − Coupon paid; Carrying value rises by this amount each period.
Premium amortization: Amortization = Coupon paid − Interest expense; Carrying value falls by this amount each period.
Ending carrying value: Ending = Opening + Interest expense − Coupon paid; Works for both discounts and premiums. It reaches face value at maturity.
Issue price: Price = PV of coupons + PV of face value, discounted at the market yield; Equals the opening carrying value.
Straight-line amortization: Per period = (Face − Issue price) ÷ number of periods, for a discount; (Issue price − Face) ÷ number of periods, for a premium; Interest expense = coupon ± this fixed amount. Expense is constant.

How to solve Effective Interest Rate Method and Amortization questions

Use this routine for any question on bond interest expense, amortization or carrying value.

1Identify the issue price (opening carrying value) and the market yield at issuance. Compute the price from the cash flows if it is not given.
2Work out the period length. For semiannual coupons, halve the annual yield and coupon rate and double the number of periods.
3Compute the cash coupon: face value × coupon rate per period.
4Compute interest expense: opening carrying value × market yield per period.
5Find amortization as the difference between interest expense and coupon. For a discount, expense is higher than coupon. For a premium, it is lower.
6Update the carrying value: opening + expense − coupon. Repeat for each period you need.
7Sanity check: a discount bond's carrying value rises toward face, a premium bond's falls toward face. If your numbers move the other way, redo them.
8If the question asks about straight-line, divide the total discount or premium by the number of periods and add or subtract it from the coupon.

Quickest way: Direction check and one-period rollforward

When to use it: Use when the question asks about one specific period or only the direction of change, such as which method gives higher expense in the early years.

Decide discount or premium: coupon rate below market yield means discount, above means premium.
Discount: carrying value and interest expense rise over time under the effective method. Premium: both fall.
Early-year expense under the effective method versus straight-line: for a discount, the effective method gives lower early expense. For a premium, it gives higher early expense.
For a specific period, do one multiplication (opening value × yield) and one subtraction. Do not build the full schedule.
Check the price on the calculator if needed. BA II Plus: N = periods, I/Y = market yield per period, PMT = coupon, FV = face, CPT PV. HP 12C: n, i, PMT, FV, then PV. Ignore the sign of the answer.

Common mistakes in Effective Interest Rate Method and Amortization

Using the coupon rate to compute interest expense.
The coupon rate is the number printed on the bond, so it feels like the interest rate.
Fix: Coupon rate gives only the cash paid. Interest expense always uses the market yield at issuance applied to the carrying value.
Multiplying the yield by face value instead of carrying value.
Students confuse the base for the coupon with the base for the expense.
Fix: Coupon = face × coupon rate. Expense = carrying value × market yield. Write both lines every time.
Getting the direction of amortization wrong for a premium.
Students memorise the discount formula and apply it unchanged.
Fix: For a premium, the coupon exceeds the expense, so carrying value falls. Check that the balance moves toward face value.
Forgetting to halve the rate and double the periods for semiannual bonds.
Annual figures in the stem are used directly.
Fix: Convert everything to the payment period before any calculation: rate ÷ 2 and periods × 2.
Assuming total interest expense differs between straight-line and effective interest.
Students see different period figures and assume different totals.
Fix: Total expense over the bond's life is identical under both methods. Only the timing differs.
Treating the amortization amount as a cash flow.
Amortization appears in the schedule next to the cash coupon.
Fix: Amortization is non-cash. Cash paid is the coupon, which does not change with the method.

Worked examples

Example 1

A company issues €1,000,000 face value five-year bonds with an annual 6% coupon, when the market yield is 8%. The issue price is €920,146. Using the effective interest method, interest expense in Year 2 is closest to: A. €73,612 B. €74,701 C. €75,971

Show the solution

Year 1 interest expense = 920,146 × 0.08 = €73,612 (rounded).
Year 1 coupon = 1,000,000 × 0.06 = €60,000. Amortization = 73,612 − 60,000 = €13,612.
Carrying value at end of Year 1 = 920,146 + 13,612 = €933,758.
Year 2 interest expense = 933,758 × 0.08 = €74,701 (rounded).
Check against the others: €73,612 is the Year 1 expense. €75,971 is the straight-line expense: discount 79,854 ÷ 5 = 15,971, plus coupon 60,000.

Answer: B. €74,701

Example 2

A company issues $500,000 face value four-year bonds with an annual 7% coupon when the market yield is 6%. The issue price is $517,326. Using the effective interest method, the carrying value at the end of Year 2 is closest to: A. $509,168 B. $513,366 C. $517,326

Show the solution

Coupon = 500,000 × 0.07 = $35,000. This is a premium bond, since the coupon rate exceeds the yield.
Year 1 interest expense = 517,326 × 0.06 = $31,040 (rounded). Premium amortization = 35,000 − 31,040 = $3,960.
Carrying value end of Year 1 = 517,326 − 3,960 = $513,366.
Year 2 interest expense = 513,366 × 0.06 = $30,802 (rounded). Premium amortization = 35,000 − 30,802 = $4,198.
Carrying value end of Year 2 = 513,366 − 4,198 = $509,168.
Direction check: a premium falls toward $500,000 face value. $509,168 is consistent. $513,366 is the end of Year 1 and $517,326 is the opening value.

Answer: A. $509,168

Exam tips

Most questions ask for one period's expense or carrying value. Do one multiplication and one subtraction, not the whole schedule.
Read the stem for the yield used at issuance. Distractors often come from using the coupon rate or the face value as the base.
Know the direction rules cold: discount means rising expense and carrying value, premium means falling. This answers many conceptual questions with no calculation.
Questions on straight-line versus effective usually test timing: total expense is equal, but early-year expense differs, and the carrying value differs between methods.
Numerical options run from smallest to largest. If your answer sits at an end, check whether you picked the opening or closing balance by mistake.

Practice questions from Topics in Long-Term Liabilities and Equity

Effective Interest Rate Method and Amortization in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Effective Interest Rate Method and Amortization: frequently asked questions

What is the effective interest rate method for bonds?

It computes interest expense each period as the opening carrying value times the market yield at issuance. The difference between that expense and the cash coupon is the amortization of the discount or premium. The carrying value then moves toward face value.

What is the difference between straight-line and effective interest amortization?

Straight-line writes off the discount or premium in equal amounts, so expense is constant. The effective method ties expense to the carrying value, so expense changes each period. Total expense over the bond's life is the same under both.

Does carrying value go up or down for a discount bond?

It goes up. The expense exceeds the coupon each period, and the unpaid difference is added to the liability. It reaches face value at maturity. A premium bond's carrying value goes down.

Which method does IFRS require?

IFRS measures such bonds at amortised cost using the effective interest method. US GAAP permits straight-line only where the result is not materially different from the effective method. Level I questions use IFRS unless they say otherwise.