Loan EMI
Equated monthly installment on a loan.
Formula
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Example
A $10 000 loan at 1%/month over 12 months has an EMI of about $888.
How it works
This formula gives the fixed monthly payment that exactly repays a loan when interest is added once per month and the same payment is made at the end of every month. It comes from balancing the present value of all future payments against the amount borrowed: each installment is discounted back to today, and the sum must equal the principal. The r factor appears because each month the remaining balance grows by interest before the next payment reduces it.
When to use it
Use this when a loan is repaid in equal monthly instalments, such as personal loans, car loans, mortgages, or equipment finance. It applies when the interest rate is a constant monthly rate and payments are made regularly with no extra fees or irregular repayments included.
Worked example, step by step
Suppose you borrow $25,000 at 0.8% interest per month for 36 months. P = 25,000, r = 0.008, n = 36 Compute (1 + r)^n = (1.008)^36 1.3329 Substitute into the formula: EMI = [25,000 0.008 1.3329] / [1.3329 - 1] EMI = 266.58 / 0.3329 EMI 800.87 So the monthly payment is about $800.87.
Common mistakes to avoid
- Using the annual interest rate instead of converting it to a monthly rate first
- Forgetting that n must be the number of monthly payments, not years
- Placing the payment at the start of each month without adjusting the formula
Did You Know?
Early loan payments go mostly to interest; only in later years does the principal shrink quickly.
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