Effective vs Nominal Rate

The Core Formula

$\text{EIR} = \left(1 + \frac{r}{m}\right)^m - 1$

The effective interest rate (EIR), or effective annual rate (EAR), is the true annualised yield once compounding has been accounted for. The nominal rate is merely what the contract quotes before adjustment.

For the continuous case:

$\text{EIR} = e^r - 1$

The Classic Trap

A loan quoted as "12% per annum, compounded monthly" does not actually cost 12% per year. The real cost is:

$\left(1 + \frac{0.12}{12}\right)^{12} - 1 = 0.126825 = 12.6825\%$

Over a 1,000,000 XOF balance that is an extra 6,825 XOF of interest in year 1 — not from a higher rate, but from the compounding mechanic hidden inside the quote.

Why Banks Use Nominal Rates

Nominal rates are easier to compare across products with different frequencies. They are also the number that typically appears in loan agreements for regulatory reasons: most disclosure regimes require the "stated" or "nominal" rate to be published, even when the effective rate is the more meaningful number.

This creates an information asymmetry. A bank can offer a loan at "11.8% nominal, monthly" and a competitor at "12.0% nominal, annual." The first loan is the cheaper of the two, but only if the customer does the conversion.

Inverting the Formula

To recover the nominal rate from a quoted EIR:

$r = m \cdot \left((1 + \text{EIR})^{1/m} - 1\right)$

This comes up frequently when converting between IFRS disclosures (which report EIR) and local tax filings (which often require nominal equivalents).

Under SYSCOHADA Revised and IFRS 9

Starting with SYSCOHADA Revised (2017) and IFRS 9 (mandatory 2018), all financial instruments classified as "amortised cost" are measured using the effective interest rate — never the nominal rate. This affects:

Loans receivable and payable
Bond investments
Trade receivables with significant financing components
Debt-structured lease receivables

The next section explains what "measured using the EIR" actually means for a bond's carrying amount.