Is EMI simple or compound interest? Your loan's real rate

Is EMI simple or compound interest?

With simple interest, interest is charged only on the amount borrowed. With compound interest, unpaid interest is added to the loan and earns interest itself. An EMI loan does neither exactly: each month the bank charges interest on the balance still owed, and that month's EMI pays all of it, so nothing is left over to compound.

So it behaves like simple interest on a falling balance, paid every month. On ₹1,00,000 at 12%, month 1's interest is ₹1,000, on the full loan; month 2's is ₹921.15, on the ₹92,115 still owed. Interest would start to compound only if an EMI fell short of the month's interest and the unpaid part were added to the loan.

Is a home loan simple or compound interest in India?

A home loan works the same way: interest at the agreed rate on the balance still owed, cleared by each EMI. Lenders differ on whether they work that interest out month by month or day by day, so check your loan agreement for the method.

It could turn into interest on interest only if a floating rate rose while the EMI stayed the same, so that the EMI no longer covered the month's interest and the shortfall was added to the loan. For floating-rate EMI loans taken for personal use, RBI rules say that lengthening the tenure after a rate rise must not lead to this "negative amortisation". You can also choose a higher EMI instead.

What simple interest rate is my EMI loan?

Banks quote a yearly rate and collect a fixed EMI every month. Most of us think in simple interest instead: ₹1 lakh at 12% is ₹12,000 a year. To turn an EMI loan into that language you need two things: the total interest you pay, and what that is as a yearly percentage of the loan.

So in simple-interest terms this loan works out to 6.62% a year. That is the honest answer to "how much simple interest am I paying on the full loan?" But it is not the rate to compare with other loans. Here is why.

Why the bank's 12% becomes 6.62% in simple interest

The bank charges 12% a year, which is 1% a month, only on the money you still owe. Every EMI pays that month's interest and returns a slice of the loan, so what you owe falls every month.

In month 1 you owe ₹1,00,000, so the interest is ₹1,000 and ₹7,885 of your EMI goes back to the bank. In month 2 you owe ₹92,115, so the interest is only ₹921.15. By the last month you owe just ₹8,795.50. (The EMI formula shows how the EMI itself is worked out.)

Averaged over the year, you held about ₹55,154 of the bank's money, a little over half the loan. The interest of ₹6,618 is 12% a year of what you actually held (the reducing rate), but only 6.62% of the full ₹1,00,000 (the flat rate). Same rupees, divided two ways.

Interest on ₹1 lakh at 12% for 1 to 5 years

The flat rate hardly moves, staying between 6.49% and 6.70% however long the loan. What grows is the total interest: ₹33,476 over 60 months, because you keep the money longer. A longer loan has a smaller EMI but costs more rupees.

Which rate should you compare with a moneylender's sekda?

Compare the bank's reducing rate with sekda × 12, when the sekda loan's interest is paid every month.

A loan at ₹1 sekda with interest paid monthly costs ₹1 per ₹100 per month, which is 12% a year. The bank's 12% reducing rate costs exactly the same. In month 1 it charged ₹1,000 on ₹1,00,000: ₹1 per ₹100. In month 2 it charged ₹921.15 on ₹92,115: again ₹1 per ₹100. Per rupee per month, the two loans cost the same. (New to sekda? See what rupaye sekda means.)

• Bank at 12% reducing = ₹1 sekda. Same cost as a ₹1 sekda loan.
• Moneylender at ₹1.5 sekda = 18% a year. Dearer than the bank at 12%.
• Bank at 10.5% reducing = about ₹0.88 sekda. Cheaper than ₹1 sekda.

The common mistake is to put the flat 6.62% (₹0.55 sekda) next to ₹1 sekda and decide the bank is half the price. It is not. The flat rate looks cheap only because you give the money back a little at a time. Repay a ₹1 sekda loan the same way, in 12 equal monthly instalments with each month's interest charged only on what is still owed, and the interest comes to the same ₹6,618.

Simple interest EMI: the flat-rate method

Some lenders, and many informal ones, work out an EMI with simple interest on the full loan: add the interest for the whole term to the loan, then divide by the months. This is what a "simple interest EMI calculator" does, and it is the flat-rate method.

It looks like the bank's method but costs far more, because you keep paying interest on money you have already repaid. Say a lender or dealer offers ₹1,00,000 at "₹1 sekda", repaid in 12 equal instalments, with interest on the full loan for all 12 months.

You return part of the loan every month but keep paying interest on all of it. So "₹1 sekda flat" on instalments really costs about ₹1.79 sekda. Check any flat rate, with its fee, in the flat rate calculator, or see the full tables in flat vs reducing interest rate.

A bigger loan: ₹5,00,000 at 10.5% for 5 years

• EMI: ₹10,747 for 60 months.
• Total paid: ₹6,44,816, of which interest is ₹1,44,816.
• Flat rate: 5.79% a year (₹0.48 sekda).
• Bank's reducing rate: 10.5% a year (about ₹0.88 sekda). This is the one to compare.

Over five years you hold on average ₹2,75,840, again a little over half the loan, so the flat rate is again a little over half the bank's rate.

Processing fees raise the real rate

A fee taken at the start means you receive less but still repay EMIs on the full loan. On the same ₹5,00,000 at 10.5% for 60 months, a ₹10,000 fee leaves ₹4,90,000 in hand and makes the real rate 11.38% a year, not 10.5%. To add the fee, GST and other charges to your own loan, find the interest rate from your EMI.

What would ₹1,00,000 cost at 12% simple interest?

Borrow ₹1,00,000 at 12% simple interest and pay everything at the end of 12 months: the interest is ₹12,000. The EMI loan at the same 12% costs ₹6,618, which is ₹5,382 less.

That does not make the EMI loan cheaper. With simple interest paid at the end you keep the whole ₹1,00,000 for all 12 months. With EMIs you start giving it back after the first month and hold about ₹55,154 on average. Both cost 12% a year, ₹1 per ₹100 a month, on the money you actually have. ₹12,000 against ₹6,618 compares two different amounts of borrowing, not two prices.

Quick checklist before you take a loan

1. Ask whether the rate is reducing or flat.
2. Convert any flat rate to a reducing rate before comparing: the flat rate calculator does it.
3. To compare with a sekda loan, divide the reducing rate by 12.
4. Add the processing fee and other upfront charges.
5. For the same amount and months, the lower EMI is the cheaper loan, before fees.