How a loan EMI is calculated, and why longer loans cost more
An EMI (equated monthly instalment) looks simple: one fixed payment every month. Underneath, each payment is split differently, and that split explains why a lower EMI can cost you far more over the life of a loan.
The formula
EMI = P × r × (1 + r)ⁿ ÷ ((1 + r)ⁿ − 1)
- P is the loan amount (the principal).
- r is the monthly interest rate: the yearly rate ÷ 12 ÷ 100.
- n is the number of monthly payments.
A worked example
Take a loan of ₹5,00,000 at 10% a year for 5 years.
- r = 10 ÷ 12 ÷ 100 = 0.008333
- n = 5 × 12 = 60 payments
- (1 + r)ⁿ = 1.008333 to the power of 60 = 1.6453
- EMI = 5,00,000 × 0.008333 × 1.6453 ÷ 0.6453 = ₹10,624 (rounded)
Over 60 months you pay about ₹6,37,411 in total. That is your ₹5,00,000 back, plus about ₹1,37,411 in interest.
Where each payment goes
Interest is charged only on what you still owe. In the first month you owe the full ₹5,00,000, so:
- Interest: 5,00,000 × 0.008333 = ₹4,167
- Principal repaid: ₹10,624 − ₹4,167 = ₹6,457
Next month you owe ₹6,457 less, so the interest is slightly lower and more of the same EMI repays the loan. Early payments are mostly interest and later ones mostly principal. This is why paying a little extra early in a loan saves far more than paying it near the end.
What a longer tenure really costs
The same ₹5,00,000 at 10% over different tenures:
| Tenure | Monthly EMI | Total interest |
|---|---|---|
| 3 years | ₹16,134 | ₹80,809 |
| 5 years | ₹10,624 | ₹1,37,411 |
| 7 years | ₹8,301 | ₹1,97,250 |
Going from 5 to 7 years saves ₹2,323 a month, but adds about ₹60,000 in interest. A longer tenure can still be the right choice if a lower EMI protects your cash flow. Just compare the total interest, not only the monthly figure.
Flat rate versus reducing balance
The formula above is for a reducing-balance loan, where interest is charged on what you still owe. Some lenders quote a flat rate, which charges interest on the original amount for the whole loan.
At a 10% flat rate, ₹5,00,000 over 5 years costs 5,00,000 × 10% × 5 = ₹2,50,000 in interest. The EMI is ₹7,50,000 ÷ 60 = ₹12,500, or about ₹1,876 a month more than the reducing-balance loan at the same "10%".
Before you compare two loan offers, ask whether each rate is flat or reducing. A flat rate that looks low can cost more than a higher reducing rate.
Other things to ask the lender
- Processing fee and insurance: these may be deducted from the loan or added to it, which changes the real cost.
- Prepayment charges: ask what it costs to pay early, as this varies by loan type and lender.
- Fixed or floating rate: on a floating-rate loan, a rate change may alter your EMI or your tenure, so your total could differ from the first estimate.
The examples are arithmetic for illustration, not a loan offer or financial advice. Your lender's schedule is the final word, as it may round differently or include fees.