How a loan EMI is calculated
An EMI, or equated monthly instalment, is the fixed amount you pay each month until a loan is repaid. It looks simple, but it hides a split: every payment covers the interest that has built up and pays off a little of the loan itself. Knowing how that split works shows why a few extra payments can save so much.
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The formula
The EMI is P × i × (1 + i)^n ÷ ((1 + i)^n − 1). P is the amount borrowed. i is the interest rate for one payment period, which for monthly payments is the yearly rate divided by 12 and by 100. n is the number of payments. An equivalent way to write it is P × i ÷ (1 − (1 + i)^−n), and with a zero rate the loan is simply divided into equal parts.
A worked example
Borrow 100,000 at 6 percent a year for 30 years. The monthly rate is 6 ÷ 12 ÷ 100 = 0.005 and there are 360 payments, so the EMI is 599.55. Over the whole loan you pay 215,838.45, of which 115,838.45 is interest, more than the amount you borrowed. The last payment is 600.00, a few cents higher, because it clears the rounding left by the earlier ones.
Why early payments are mostly interest
Each month the interest is the remaining balance times the monthly rate, and whatever is left of the payment reduces the balance. At the start the balance is at its highest, so the interest is too:
| Payment | Interest | Principal | Balance after |
|---|---|---|---|
| 1 | 500.00 | 99.55 | 99,900.45 |
| 180 (halfway) | 356.46 | 243.09 | 71,048.97 |
| 360 (last) | 2.99 | 597.01 | 0.00 |
When principal overtakes interest
The payment never changes, but the interest falls as the balance falls, so the principal share grows. In this loan the principal first exceeds the interest at payment 223, after more than 18 years. That slow start is why paying off a loan early in its life saves far more than paying it off late.
A shorter loan costs far less interest
Borrow 500,000 at 10 percent for 5 years and the EMI is 10,623.52. The total interest is 137,411.38, about 27 percent of the amount borrowed, compared with about 116 percent in the 30-year example, even though the rate is higher. The longer you take, the more interest has time to build.
What an extra payment does
Take 200,000 at 5 percent for 30 years. The EMI is 1,073.64 and the total interest is 186,513.24 over 360 payments. Add 200 to every payment and the loan is cleared after 256 payments, which is 21 years and 4 months. The interest falls to 125,351.80, so you save 61,161.44 and 104 payments. The extra money goes straight to the balance, so every later month’s interest is smaller.
Flat rate and reducing balance
Some lenders quote a flat rate, where interest is charged on the original amount for the whole term. A reducing-balance rate charges it only on what you still owe. A flat rate looks lower than a reducing-balance rate for the same loan, so to compare offers, ask for the reducing-balance rate or the annual percentage rate.