The formula, stated up front
The standard Equated Monthly Instalment for a fully amortising fixed-rate loan is EMI = P × r × (1 + r)^n / ((1 + r)^n − 1), where P is the principal you borrow, r is the periodic interest rate (the annual rate divided by the number of payments per year), and n is the total number of payments over the life of the loan.
It looks like a wall of symbols. It is in fact one of the cleanest results in finance, and it falls out of a single insight: the bank is loaning you a lump sum today in exchange for a stream of identical payments in the future, and those two things must be worth the same amount once you discount the future stream back to today.
Deriving it from first principles
Suppose you borrow P today at periodic rate r, and you agree to pay an equal amount E at the end of each of the next n periods. From the bank's perspective, the present value of all your future payments must equal what they lent you.
A payment of E one period from now is worth E / (1 + r) today, because if the bank had E / (1 + r) today they could lend it out and have E in a period. Two periods away it is worth E / (1 + r)^2. So the total present value of your stream of n payments is E / (1 + r) + E / (1 + r)^2 + ... + E / (1 + r)^n.
That is a geometric series with first term E / (1 + r) and common ratio 1 / (1 + r). Summing it gives E × (1 − (1 + r)^−n) / r. Set that equal to P, solve for E, and after a little algebra you land on E = P × r × (1 + r)^n / ((1 + r)^n − 1). That's it. The intimidating EMI formula is just the inverse of the present-value-of-an-annuity sum.
How interest and principal split each month
Your EMI is constant, but its composition is not. Each month, the bank first charges interest on the outstanding balance at rate r. Whatever is left of your EMI after that goes to reducing the principal. Next month the balance is smaller, so the interest portion is smaller, so more of the EMI goes to principal — and so on.
Concretely: borrow 1,000,000 at 8 percent annual interest over 20 years. r is 0.08/12 ≈ 0.00667, n is 240. EMI works out to roughly 8,364. In month one, interest is 1,000,000 × 0.00667 = 6,667, leaving only 1,697 for principal. By month 120 (the half-way point), the split is roughly 4,800 interest and 3,500 principal. By month 240, almost the entire EMI is principal.
This is why the first ten years of a 20- or 30-year mortgage feel like you're barely chipping the balance: you mostly are. The bank is collecting the interest you owe on the large balance you started with.
Why a 30-year and a 15-year loan at the same rate are not comparable
Take the same 1,000,000 principal at 8 percent. Over 15 years (n = 180) the EMI is about 9,557. Over 30 years (n = 360) it is about 7,338. The 30-year loan is gentler by 2,219 a month — but it costs you 1,641,000 in total interest, against 720,000 for the 15-year loan. You pay more than twice as much for the privilege of a smaller monthly payment.
That ratio is not a quirk of these numbers; it's the mechanics of compound interest acting over a longer horizon on a larger average balance. The 30-year loan keeps a high balance for longer, and the bank earns 8 percent on that balance every year.
This is not an argument that longer terms are wrong. They can be exactly right — they keep monthly obligations within reach and free cashflow for other things. But you should know the price of the optionality.
Prepayment math: one extra payment a year is genuinely a lot
Here is the result that surprises everyone the first time they see it: on a 30-year mortgage, paying one extra EMI per year — thirteen payments instead of twelve — typically knocks four to six years off the loan and saves a quarter of the total interest. It is not a marketing exaggeration; it falls straight out of the amortisation arithmetic.
The reason it works so well is that every extra rupee you put down early kills compound interest in the back half of the loan. A 1,000 prepayment in year three of a 30-year loan at 8 percent does not just save 1,000; it saves the 27 years of compounding interest that 1,000 would have generated. The further from the end of the loan you prepay, the more leverage each rupee has.
APR is not the interest rate
The advertised interest rate on a loan is the rate that goes into the EMI formula. The APR — Annual Percentage Rate — is something different and usually higher: it bundles in mandatory fees (origination fee, processing fee, points, certain insurance) and re-expresses the total cost as an effective annual rate.
Two loans with the same headline interest rate can have very different APRs if one charges 2 percent in origination fees and the other charges nothing. APR is the regulator's attempt to give you a single number you can use to compare offers honestly. When you compare loan offers, compare APR to APR. When you compute your EMI, use the actual interest rate, not the APR.
Use SnapToolz's loan calculator to plug in your real numbers, then play with the inputs: what happens if you shorten the tenure by five years? What happens if you add a 50,000 prepayment in year three? Five minutes with a calculator can save you years of payments. For the limits of any financial information on this site, see our /disclaimer/. Nothing here is financial advice.
Tools used in this guide
FAQ
- Why is the interest portion of my EMI so high in the early months?
- Because interest each month is charged on the entire outstanding balance, and at the start of the loan the balance is essentially the full principal. The EMI is fixed, so once interest is deducted there is very little left for principal. As the balance falls each month, the interest portion falls and the principal portion grows.
- Is it always worth prepaying my loan?
- Mathematically, prepayment saves interest at exactly your loan's interest rate. So the question is whether the same money invested elsewhere would earn more after tax than your loan rate. If your loan is at 8 percent and you can reliably get 6 percent after tax in a safe investment, prepay. Also check for prepayment penalties — some loans charge a fee that erodes the benefit.
- Why is the APR on my loan higher than the interest rate?
- Because APR includes mandatory fees — origination fees, processing fees, points, sometimes insurance — that the headline interest rate ignores. APR re-expresses the true cost of borrowing as an effective annual rate so you can compare two offers fairly. Always compare APR to APR; use the interest rate (not APR) when you actually compute the EMI.
- Can the same EMI formula handle car loans, personal loans, and mortgages?
- Yes, as long as they're fixed-rate, fully-amortising, and pay an equal amount each period. The principal, rate, and tenure differ, but the math is identical.