Effective interest rate

The term effective interest rate carries three different meanings, and confusing them is the single most common error in discussions of loan pricing and reporting.

• Effective annual rate (EAR) - What it measures: A nominal rate adjusted for compounding frequency

  • Where it is used: Comparing deposits and loans with different compounding periods

• Effective interest rate under IFRS 9 (EIR) - What it measures: The rate that spreads fees and transaction costs over a loan's expected life

  • Where it is used: Financial reporting and interest income recognition

• Colloquial "effective rate" - What it measures: What a loan really costs, all in

  • Where it is used: Usually a loose synonym for APR

The first is arithmetic. The second is accounting. The third is a disclosure concept covered on the APR page. This page deals with the first two.

Meaning 1: the effective annual rate

A nominal rate does not state how often interest compounds. Two products quoting 12% per annum can produce different amounts of interest depending on whether that 12% is applied once a year or in twelve monthly instalments of 1%.

The effective annual rate converts a nominal rate into what it actually yields over a year:

EAR = (1 + i ÷ n)^n − 1

where  i = nominal annual rate
       n = compounding periods per year

12% nominal at different compounding frequencies

• Annually (1 period): 12.000%
• Semi-annually (2 periods): 12.360%
• Quarterly (4 periods): 12.551%
• Monthly (12 periods): 12.683%
• Daily (365 periods): 12.748%
• Continuously (∞): 12.750%

Two observations follow. More frequent compounding always produces a higher effective rate, and the increases get smaller each time — the sequence converges on e^i − 1, which is the continuous compounding ceiling. Beyond monthly, the additional effect is small.

Converting back

To find the nominal rate that produces a given effective rate:

i = n × [ (1 + EAR)^(1÷n) − 1 ]

Where it matters

• Savings and deposits. Comparing a 6% quarterly-compounding deposit against a 6.1% annually-compounding one requires converting both to effective rates.
• Credit cards and revolving credit, where interest is typically compounded monthly on an outstanding balance.
• Any comparison across products with different compounding conventions — the nominal figures simply are not comparable.

Note that a standard amortising loan repaid in monthly instalments does not compound in this sense, because interest is paid each period rather than added to the balance. Compounding matters where interest is capitalised — during a payment holiday, on arrears, or on a deposit.

Meaning 2: EIR under IFRS 9

In financial reporting, the effective interest rate has a precise technical definition: the rate that exactly discounts estimated future cash flows through the expected life of a financial asset to its gross carrying amount at initial recognition.

Its purpose is to prevent fee income being recognised at disbursement. Instead, fees and transaction costs are absorbed into a single rate and released across the life of the loan.

What goes into the EIR

Included:

• Origination, initiation and arrangement fees received from the borrower
• Directly attributable incremental transaction costs paid — commission, legal, valuation
• Any premium or discount on acquisition
• Points paid or received that form part of the yield

Excluded:

• Expected credit losses, for assets that are not credit-impaired on purchase
• Fees for distinct services delivered separately over time
• Administrative overheads not directly attributable to originating the specific loan

Worked example

A $10,000 loan over 36 months at a contractual 15% per annum, with a $300 origination fee received and $100 of directly attributable costs paid.

Contractual instalment            = $346.65
Initial net carrying amount       = 10,000 − 300 + 100 = $9,800

The EIR is the rate discounting those 36 payments of $346.65 back to $9,800:

Contractual rate  = 15.0% per annum
EIR               ≈ 16.4% per annum (nominal), ≈17.7% effective

The lender's reported interest income reflects 16.4%, not 15%, and the $300 fee is never recognised as a lump sum. It emerges gradually as part of interest revenue over three years.

How it is applied

Interest revenue for the period = amortised cost × EIR

Two refinements matter in practice:

• Credit-impaired assets (Stage 3). Interest is calculated on the net carrying amount — after deducting the loss allowance — rather than the gross amount. Continuing to accrue on the gross balance of an impaired loan overstates income.
• Modification. Where a loan is restructured without derecognition, the carrying amount is recalculated by discounting the revised cash flows at the original EIR, with the difference taken to profit or loss immediately. The EIR itself is not reset.

Why it matters operationally

Recognising origination fees as income at disbursement is a common error in smaller lenders. It:

• Overstates profit in the period the loan is written
• Understates it across the remaining term
• Inflates apparent yield on new business
• Produces results that flatter a growing book and reverse sharply when growth slows

That reversal pattern is a recurring cause of restated microlender accounts.

Effective interest rate versus APR

The two are related but serve different purposes, and one does not substitute for the other.

• Effective interest rate (EIR): - Defined by: Accounting standards (IFRS 9)

  • Audience: Preparers and users of financial statements
  • Purpose: Recognising interest income over time
  • Fee treatment: Fees integral to yield, net of transaction costs
  • Basis: Expected loan life

• Annual Percentage Rate (APR): - Defined by: Consumer credit regulation

  • Audience: Borrowers comparing loan offers
  • Purpose: Disclosing the all-in cost of credit
  • Fee treatment: All compulsory borrower charges
  • Basis: Contractual schedule, usually

They frequently produce different numbers for the same loan, legitimately. APR captures every mandatory charge the borrower bears, including some that never reach the lender — compulsory insurance premiums paid to a third party, for instance. EIR captures only what enters the lender's yield, net of its own costs.

Common errors

• Comparing a nominal rate to an effective rate. They are not the same measure; convert first.
• Annualising by multiplying by twelve where interest capitalises. A 2% monthly rate on a capitalising balance is 26.8% effective, not 24%.
• Assuming a monthly instalment loan compounds. It generally does not — interest is paid, not added.
• Recognising fees upfront instead of amortising them through the EIR.
• Accruing interest on the gross carrying amount of a credit-impaired exposure.
• Resetting the EIR on modification where the standard requires the original rate to be retained.