EMI = P × r × (1 + r)n ÷ [(1 + r)n − 1], where P is the loan amount, r the monthly interest rate (annual rate ÷ 12 ÷ 100) and n the number of months. A loan of 1,000,000 at 12% a year for 5 years has r = 0.01 and n = 60, giving an EMI of about 22,244 and total interest of about 334,667.
An EMI (equated monthly instalment) is the fixed amount you pay each month on a loan. It feels simple: the same number on the same date. Behind it is a formula that decides how much of each payment is interest and how much actually reduces your debt, and that split surprises most borrowers.
The EMI formula
EMI = P × r × (1 + r)n ÷ [(1 + r)n − 1]
- P = principal, the amount you borrow
- r = monthly interest rate = annual rate ÷ 12 ÷ 100
- n = number of monthly instalments = years × 12
This is the reducing balance method used for most bank loans, home loans and car finance quoted with an APR. Interest each month is charged only on what you still owe.
A worked example
Loan of 1,000,000 at 12% a year for 5 years. (The currency doesn’t matter: rupees, dirhams, dollars all work the same.)
- Monthly rate:
12 ÷ 12 ÷ 100 = 0.01
- Months:
5 × 12 = 60
- (1 + r)n:
1.0160 ≈ 1.8167
- EMI:
1,000,000 × 0.01 × 1.8167 ÷ (1.8167 − 1) = 18,167 ÷ 0.8167 ≈ 22,244
- Total paid:
22,244 × 60 ≈ 1,334,667, so total interest ≈ 334,667
A loan calculator does this instantly and shows the full schedule, but it’s worth doing once by hand to see where the numbers come from.
Where each payment goes
The EMI never changes, but its make-up does. In month 1 you owe the full 1,000,000, so interest is 1% of that: 10,000. Only 12,244 of your payment reduces the loan. Each month the balance is a little lower, so the interest part shrinks and the principal part grows.
| Month | EMI | Interest | Principal | Balance after |
|---|---|---|---|---|
| 1 | 22,244 | 10,000 | 12,244 | 987,756 |
| 2 | 22,244 | 9,878 | 12,367 | 975,389 |
| 30 | 22,244 | about 5,900 | about 16,340 | about 574,100 |
| 60 | 22,244 | about 220 | about 22,024 | 0 |
Halfway through the term, you’ve repaid well under half the loan. That’s normal for reducing-balance loans, and it’s why paying extra early has such a strong effect.
Longer tenure: smaller EMI, bigger bill
| Same 1,000,000 at 12% | EMI | Total interest |
|---|---|---|
| 3 years | 33,214 | 195,715 |
| 5 years | 22,244 | 334,667 |
| 20 years | 11,011 | 1,642,607 |
Stretching from 5 to 20 years halves the EMI but multiplies the interest by almost five. A longer tenure is sometimes the right choice for cash flow, but go in knowing the price.
What prepayment does
Any extra amount you pay goes straight to the principal. Lower principal means less interest every following month. Lenders usually let you choose between keeping the EMI and shortening the term (saves the most interest) or keeping the term and lowering the EMI. Check whether your loan has a prepayment charge; many floating-rate home loans don’t.
What the EMI doesn’t show
- Processing fees and insurance added to the loan or charged upfront.
- Flat-rate quotes that look cheaper than they are. A 10% flat rate costs far more than a 10% reducing rate; see flat vs reducing interest rates.
- Floating rates that change over time, which usually changes the term or the EMI.
- Islamic financing structures such as diminishing musharakah use rental and purchase payments instead of interest, but the monthly amounts are often worked out in a similar way.
Frequently asked questions
What is the formula for EMI?
Why is most of my early EMI interest?
Does a longer loan term save money?
Is it better to reduce EMI or tenure after a prepayment?
Is EMI calculated on a flat or reducing balance?
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