Loan & EMI formulas, explained clearly
Every calculator on this site is just arithmetic you can do yourself. This page lays out each formula we use — what every symbol means, a worked example with real Indian numbers, and a plain-language explanation of why it works. No black boxes.
Jump to: EMI · Amortization · Total interest · Prepayment saving · Balance-transfer break-even · Affordability (reverse EMI) · FOIR · Step-up EMI · Rate sensitivity · Flat vs reducing rate
1. The EMI formula
This is the single most important formula in personal finance, and the engine behind every loan on this site. It converts a loan amount, an interest rate and a tenure into one fixed monthly payment.
| P | Principal — the loan amount you borrow |
| r | Monthly interest rate = annual rate ÷ 12 ÷ 100 |
| n | Number of monthly instalments = years × 12 |
Worked example. A ₹50,00,000 home loan at 8.5% for 20 years:
- r = 8.5 ÷ 12 ÷ 100 = 0.007083
- n = 20 × 12 = 240
- (1 + r)n = 1.007083240 = 5.4412
- EMI = 50,00,000 × 0.007083 × 5.4412 ÷ (5.4412 − 1) = ₹43,391
Why this shape? The numerator is what the balance would grow to with interest; the denominator spreads that cost evenly so every month's payment is identical. If the rate is 0%, the formula collapses to the simple P ÷ n.
Try it on the home loan calculator →
2. Amortization — how each EMI splits
Your EMI is fixed, but the split between interest and principal changes every month. Each month:
Worked example (month 1 of the loan above). Interest = 50,00,000 × 0.007083 = ₹35,417; principal = 43,391 − 35,417 = ₹7,974; new balance = ₹49,92,026. Early on, almost all of your EMI is interest. As the balance shrinks, the interest portion falls and the principal portion grows — which is why the last few years of any loan clear the balance rapidly.
More on why early EMIs are mostly interest →
3. Total interest payable
You pay the EMI n times; subtract the original principal and what remains is the lender's interest. For our example: 43,391 × 240 − 50,00,000 = ₹54,13,879. Over 20 years you repay more in interest than you borrowed — which is exactly why prepayment and a lower rate matter so much.
4. Prepayment saving
A prepayment is a lump sum paid over and above your EMI. It goes 100% against the outstanding balance, so every future month's interest is charged on a smaller amount. There is no single closed-form figure — you re-run the amortization from the prepayment month with a reduced balance and compare total interest with and without it.
Two levers decide the size of the saving: how much you prepay and how early. Earlier is dramatically better, because the reduced balance has more remaining months over which to compound the saving. You then choose to either reduce the tenure (keep EMI same, finish sooner — usually the bigger saving) or reduce the EMI (keep tenure, lower monthly outgo).
Open the prepayment optimizer →
5. Balance-transfer break-even
Switching your loan to a lower rate has an upfront cost (processing, legal, stamp). The break-even tells you how many months of EMI saving it takes to recover that cost.
Both EMIs are computed on the same outstanding balance and remaining tenure — only the rate differs. If the break-even lands comfortably inside your remaining tenure, the switch pays off. Since RBI bars foreclosure charges on floating-rate home loans, leaving your old bank is effectively free, so the decision rests on the rate gap versus the new lender's processing cost.
Open the balance-transfer calculator →
6. Affordability — the EMI formula in reverse
If you know the EMI you can afford, you can solve the EMI formula backwards for the largest loan that fits:
This is the same equation rearranged to make P the subject. Banks decide your affordable EMI from your income using FOIR (next section).
Open the affordability calculator →
7. FOIR — Fixed Obligation to Income Ratio
This is how lenders cap your borrowing. It is the share of your take-home income already committed to all loan EMIs. Most banks want FOIR to stay under 50% (sometimes up to 60–65% for high earners). If your existing EMIs plus the proposed new EMI push FOIR past the limit, the loan is trimmed or rejected — regardless of how good your CIBIL score is.
Check your FOIR across all loans →
8. Step-up EMI
A step-up loan starts with the standard EMI, then raises it by a fixed percentage each year (matching expected salary growth). Each year's EMI is:
where g is the annual step-up rate (e.g. 5%). Because more principal is cleared in later years, a step-up loan finishes faster and costs less total interest than a flat EMI on the same amount — useful for young borrowers whose income will rise.
9. Rate sensitivity (the repo shock)
Indian floating-rate loans move 1:1 with the RBI repo rate. When the rate changes, your bank either raises the EMI (tenure fixed) or extends the tenure (EMI fixed). The new EMI is simply the EMI formula recomputed at the new rate:
where r′ is the new monthly rate after the shock. The tenure-extension case is non-linear: as the rate rises toward the point where your old EMI barely covers the monthly interest, the tenure stretches sharply — and beyond that point the loan can never clear at the old EMI.
Open the rate-sensitivity calculator →
10. Flat rate vs reducing balance
This is the trap behind many car and personal loan adverts. A reducing-balance rate (what the EMI formula above uses) charges interest only on the outstanding balance. A flat rate charges interest on the full original principal for the entire tenure:
A "9% flat" loan is not a 9% loan. Its true reducing-rate equivalent is usually close to 1.8× the flat number — so 9% flat is roughly 16% reducing. Always ask lenders for the reducing-balance rate (the APR), and compare on that.
Why bank EMIs differ from calculators →
A note on rounding
Banks round the EMI to the nearest rupee, and some compute interest on a daily or actual-days basis rather than a clean monthly rate. That can shift the EMI by a few rupees and the total interest by a little over a long tenure. Our calculators use the standard monthly-rate convention, which matches the vast majority of Indian home loan sanction letters. For the exact figure on your specific loan, always check the amortization schedule your lender provides.