Interest rate converter (monthly ↔ annual)

Two rates are equivalent when they yield exactly the same over the period. The classic mistake is multiplying or dividing by 12 — that gives the "nominal" rate, which ignores interest on interest.

The right path goes through the effective annual rate:

i_year = (1 + i)periods per year − 1

And back (annual → monthly) uses the root:

i_month = (1 + i_year)1/12 − 1

Step-by-step example

1%/month is not 12%/year:

• (1.01)¹² − 1 = 12.68%/year

Why it matters

Comparing a "2%/month" loan with a "26%/year" one only works once both are on the same basis. (2%/mo = 26.8%/yr.)