Finance

Loan Payment (EMI)

Formula

EMI = P × r × (1+r)ⁿ / ((1+r)ⁿ − 1)

What is Loan Payment (EMI)?

The Equated Monthly Installment (EMI) formula calculates the fixed monthly payment for a loan. P is the principal, r is the monthly interest rate, and n is the number of monthly payments.

Variables

P
P — Principal loan amount
r
r — Monthly interest rate (annual rate / 12 / 100)
n
n — Total number of monthly payments

Worked Examples

Example 1

Find the monthly payment for a $10,000 loan at 12% annual interest for 3 years.

Solution:

r = 12/12/100 = 0.01, n = 36. EMI = 10000 × 0.01 × (1.01)³⁶ / ((1.01)³⁶ − 1) = 10000 × 0.01 × 1.4308 / 0.4308 ≈ $332.14/month

Frequently Asked Questions

Related Formulas

Future Value (Compound Interest)

FV = PV × (1 + r/n)^(n×t)

PV = FV / (1 + r)ⁿ

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