What is the EAR formula in real estate finance?

The effective annual rate (EAR) tells you how much a balance grows over one year after interest compounds. For a nominal annual rate r compounded n times per year, the formula is EAR = (1 + r/n)^n − 1. Enter r as a decimal. Monthly compounding means n = 12, no matter how many years the loan runs.

Work it out on a $10,000 balance

Suppose a balance accrues interest at a nominal 12% and unpaid interest is added monthly. The monthly rate is 0.12 ÷ 12 = 0.01. After one year, (1.01)^12 − 1 is about 0.1268: an EAR of 12.68%. With no payments or fees, $10,000 becomes about $11,268. At the same nominal rate compounded only once a year, it becomes $11,200. The $68 difference is interest on earlier interest.

When is EAR the wrong comparison?

An amortizing mortgage does not let the entire balance grow untouched for a year. If interest is paid monthly and never capitalized, the example does not describe the dollars you will actually pay. EAR also does not automatically include origination fees, points or a rate change. Compare the actual payments and fees over the expected holding period. OpenStax’s compound-interest examples explain the underlying math; for a loan funded in stages, see commercial construction loan rates.