How to convert interest rates (monthly ↔ annual)

The most common interest mistake is multiplying or dividing the rate by 12. That gives the nominal rate, which ignores interest on interest. For correct comparisons, use equivalent (effective) rates.

The formula

From a per-period rate to the effective annual rate:

i_year = (1 + i)periods per year − 1

The reverse (annual → monthly) uses the root:

i_month = (1 + i_year)1/12 − 1

Step-by-step example

1%/month is not 12%/year. It's:

(1.01)12 − 1 = 0.1268 = 12.68%/year

In reverse, 12%/year equals (1.12)^1/12 − 1 ≈ 0.949%/month — not 1%.

Why the difference exists

Because compound interest earns on interest already accrued. The more periods, the wider the gap between the "added" (nominal) rate and the real (effective) rate.

Why it matters

Comparing a "2% per month" loan with a "26% per year" one only works if you convert both to the same basis. (2%/month = 26.8%/year — pricier than it looks.)

FAQ

Nominal vs effective rate? Nominal just adds/divides linearly; effective accounts for compounding and reflects the true cost.