When you take out a loan, the bank tells you your Equated Monthly Installment (EMI)—the amount you must pay every month. But have you ever wondered how they come up with that number?
Understanding the math can help you spot errors and better understand how interest rates and loan terms affect your wallet.
The EMI Formula
The standard formula for calculating EMI is:
E = P x r x (1 + r)^n / ((1 + r)^n - 1)
Where:
- E = EMI (Monthly Payment)
- P = Principal Loan Amount
- r = Monthly Interest Rate (Annual Rate / 12 / 100)
- n = Loan Tenure in Months
Step-by-Step Example
Let's calculate the EMI for a $10,000 loan at 12% annual interest for 3 years (36 months).
-
Calculate Monthly Rate (r):
- 12% per year / 12 months = 1% per month.
- 1% = 0.01
-
Apply the Formula:
- E = 10,000 x 0.01 x (1 + 0.01)^36 / ((1 + 0.01)^36 - 1)
- E = 100 x (1.01)^36 / ((1.01)^36 - 1)
- E = 100 x 1.4307 / (1.4307 - 1)
- E = 143.07 / 0.4307
- E ≈ $332.14
So, your monthly payment would be $332.14.
How to Calculate in Excel
You don't need to do this math by hand! In Excel or Google Sheets, use the PMT function:
=PMT(rate, nper, pv, [fv], [type])
- rate: Annual Interest Rate / 12
- nper: Total number of months
- pv: Loan amount (Principal)
Example:
=PMT(12%/12, 36, -10000)
(Note: Put the loan amount as a negative number to get a positive result).
Why Use a Calculator?
Manual calculation is good for understanding, but it's prone to errors. Our Loan Calculator does this instantly and also shows you the Amortization Schedule (how much of your payment goes to interest vs. principal each month).
Try it now to check your bank's numbers!
Written by Calc Labo Research Team