How EMI Is Calculated: The Formula Explained With Worked Examples

Your bank quotes a monthly number — Rs. 52,992 for that car loan, Rs. 41,000 for the home loan — and most people just accept it. But that number comes from a precise formula, and knowing it lets you verify the bank's maths, compare offers honestly, and see exactly how much interest you're really paying. Here's the EMI formula, explained step by step with worked Pakistani examples.

The EMI formula

EMI stands for Equated Monthly Instalment — the fixed amount you pay every month until the loan is cleared. The formula lenders use is:

E = P × r × (1 + r)ⁿ / ((1 + r)ⁿ − 1)

Each symbol means something concrete:

• E — the EMI, your monthly payment (what we're solving for)
• P — the principal, the amount you borrow
• r — the monthly interest rate (annual rate ÷ 12)
• n — the number of monthly payments (years × 12)

The single most common mistake is plugging the annual rate into r. A 20% annual rate means r = 0.20 ÷ 12 = 0.016667 per month, not 0.20. Get that wrong and your answer will be wildly off.

Worked example: a Rs. 2,000,000 car loan

Let's run a realistic Pakistani example: a Rs. 2,000,000 car loan at 20% annual interest over 5 years — typical of bank auto finance rates in 2026.

Step 1 — convert to monthly terms.
r = 0.20 ÷ 12 = 0.016667
n = 5 × 12 = 60 payments

Step 2 — compute (1 + r)ⁿ.
(1.016667)⁶⁰ ≈ 2.6960

Step 3 — plug into the formula.
E = 2,000,000 × 0.016667 × 2.6960 ÷ (2.6960 − 1)
E = 2,000,000 × 0.016667 × 2.6960 ÷ 1.6960
E = 33,333.33 × 2.6960 ÷ 1.6960
E ≈ Rs. 52,992 per month

Step 4 — sanity-check the total.
60 payments × Rs. 52,992 = Rs. 3,179,520 total paid.
Minus the Rs. 2,000,000 principal = Rs. 1,179,520 in interest — about 59% on top of what you borrowed. That interest figure surprises most first-time borrowers, and it's exactly why the formula matters.

Run your own numbers: Plug your loan amount, rate and tenure into our free EMI calculator to verify any bank quote in seconds.

Where your money goes: principal vs interest each month

Your EMI stays constant, but its composition changes every month. Early on, you're mostly paying interest; toward the end, mostly principal. Here's our Rs. 2,000,000 example:

This is the reducing-balance method: interest is charged each month only on the remaining balance, so as you pay down principal, the interest slice shrinks.

What changes your EMI: the tenure trade-off

Same Rs. 2,000,000 loan at 20%, three different tenures:

Stretching from 3 to 7 years cuts the monthly payment by 40% — but you pay 2.5x the interest. Take the shortest tenure whose EMI fits comfortably in your budget.

Flat rate vs reducing balance: why the quoted rate can mislead

Pakistani lenders sometimes advertise a "flat" or "add-on" rate that looks cheaper than a reducing-balance rate — and comparing them directly is a trap. Under a flat-rate quote, interest is charged on the full original principal every month, even though you're steadily repaying it.

Take our Rs. 2,000,000 loan at a "flat 10%" for 5 years: flat interest = 2,000,000 × 10% × 5 = Rs. 1,000,000, giving a monthly payment of (2,000,000 + 1,000,000) ÷ 60 = Rs. 50,000. That sounds cheaper than our 20% reducing-balance EMI of Rs. 52,992 — but the true reducing-balance equivalent of that flat quote is roughly 17–18%, barely below 20%. Rule: never compare a flat quote against a reducing-balance quote — convert first, or just compare EMIs and total interest side by side. We'll unpack this fully in our upcoming flat rate vs reducing balance guide.

Also watch for add-on costs that never appear in the EMI formula: processing fees (often 1–2% of the loan), documentation charges, and mandatory credit-life insurance, which banks in Pakistan commonly bundle into auto and personal loans. A Rs. 2,000,000 loan with a 1.5% processing fee costs Rs. 30,000 before the first EMI is even due — always add fees to the total cost when comparing two offers.

Common mistakes when checking an EMI

• Using the annual rate as the monthly rate. Always divide by 12 first.
• Comparing EMIs without comparing total interest. A lower EMI over a longer tenure almost always costs more overall.
• Ignoring fees. Processing fees, documentation charges and mandatory insurance add to the true cost. Add them to the total before comparing offers.
• Confusing flat-rate quotes with reducing-balance EMIs. Some lenders quote a "flat" rate that sounds lower but is charged on the full principal every month — far more expensive than the same number as a reducing-balance rate.
• For dollar earners: if part of your income is in USD, exchange-rate swings change what your EMI really costs you — see our interbank vs open market dollar rate explainer.

FAQs

What is the formula to calculate EMI?

E = P × r × (1+r)n / ((1+r)n − 1), where P is the loan amount, r is the monthly interest rate (annual rate ÷ 12), and n is the number of monthly payments. For example, a Rs. 2,000,000 loan at 20% annual interest over 5 years gives an EMI of about Rs. 52,992.

How do I convert an annual interest rate to a monthly rate for EMI?

Divide the annual rate by 12. A 20% annual rate becomes 0.20 ÷ 12 = 0.016667 per month. Never plug the annual rate directly into the formula — that is the most common EMI calculation mistake.

Does a longer loan tenure always mean more interest paid?

Yes, at the same interest rate. On a Rs. 2,000,000 loan at 20%, stretching from 3 to 7 years cuts the EMI from Rs. 74,326 to Rs. 44,413 but raises total interest from about Rs. 676,000 to Rs. 1,731,000 — roughly 2.5 times more.

Why does my EMI stay the same but the interest portion shrink?

Because of the reducing-balance method: each month's interest is charged only on the remaining loan balance. As you repay principal, the balance — and therefore the interest slice — shrinks, so more of each fixed EMI goes toward principal over time.

Are bank EMI calculators accurate?

The maths is standard, so any correct calculator gives the same EMI for the same inputs. Differences between quotes come from the inputs: the exact rate, whether fees are included, and whether the quote uses reducing-balance or flat-rate method. Verify with our EMI calculator using the bank's own stated rate and tenure.