Loan and EMI: What an Instalment Is Made Of, Month by Month

The calculator here works out the equated monthly instalment (EMI) on a borrowing and shows what each instalment is made of. Put in the amount, the tenure in months, the contracted rate and the basis that rate is quoted on, and it returns the monthly instalment, the total repayable across the whole tenure, and the split of every single instalment between the part that clears the debt and the part that pays the charge.

Because a figure that lives only inside a panel is invisible to anyone who cannot run it, here are its opening readings in ordinary text. On Rs 82,000/- over thirty months at 11.2913 per cent a year the instalment is Rs 3,150/-, the total repayable is Rs 94,500/-, and Rs 12,500/- of that total is charge. Instalment 1 is Rs 772/- of charge against Rs 2,378/- reaching the debt. Instalment 15 is Rs 438/- against Rs 2,712/-, leaving Rs 43,875/- owed. Instalment 30 is Rs 29/- against Rs 3,121/-, and it closes the loan at nil. The same borrowing quoted the other way round is 6.10 per cent a year flat.

A loan's definition, the names of its charges and the reason a lender charges anything at all are covered separately. The work here is arithmetic: three numbers go in, two numbers come out, and thirty rows of a schedule come out with them.

The borrowing the panel opens on belongs to the Bhosale household, and they have been paying it for two years. A two-wheeler priced at Rs 96,000/-, Rs 14,000/- put down, Rs 82,000/- borrowed, thirty months to repay it, and Rs 3,150/- leaving the account on the 7th of every month. The loan cleared in January of the second year on its thirtieth instalment, exactly on the schedule it was signed with.

A cost and a judgement are different things. Arithmetic settles what a borrowing costs, and nothing in the arithmetic settles whether the borrowing was a good idea. A household that borrowed to keep a counter open, or to reach work, or because the alternative was worse, did not make a mistake that a calculator can detect.

What does this working tool compute?

Three numbers read off the agreement, two headline outputs, and one table. The three numbers are the amount borrowed, the number of months and the contracted rate. Two further fields carry the basis that rate is quoted on and the total the agreement itself states, so the panel can check its own answer back against the paper it came from. The two outputs are the monthly instalmentThe fixed monthly payment on a loan, the same amount every month for the whole run of the borrowing. and the total repayable. The table is what neither of those numbers can show on its own: what each instalment is made of, month by month, from the first to the last.

Think of a kirana shopkeeper who lets a customer pay off a big purchase in fixed weekly amounts. Every week the same note is handed over. But the shopkeeper is keeping two columns in the notebook, not one: how much of that note settled the goods, and how much of it was the price of being allowed to pay late. The note is one number. The notebook has two. An instalment is one payment carrying two jobs, and the whole point of this tool is that it shows both jobs rather than only the payment.

Which numbers go in, and where is each one found?

A tool is only as good as what is typed into it, so every field in the panel carries a field noteThe short line under an input naming the document the figure is read off, so the number comes from paper rather than from memory.. A field note does one job and no other: it names the document the number is read off. A field note does not say what the number means, and it does not say whether the number is good.

Input one: the amount borrowed

The figure that goes in is what the lender lends, not what the thing costs. The Bhosale household bought a two-wheeler priced at Rs 96,000/- and put Rs 14,000/- down, so Rs 82,000/- is the borrowing and Rs 96,000/- is not. Field note: the amount is read off the sanction letter or the opening sheet of the agreement, on the line that names a sum being lent. Where a charge is deducted before the money moves, the sum that reaches the borrower is smaller than the sum being lent, and it is the sum being lent that the schedule is built on.

Input two: the tenure in months

The tenureThe number of months a loan runs for, counted from the first instalment to the last. that goes in is the number of instalments the agreement schedules, in months. Thirty here. Field note: the tenure is read off the repayment schedule attached to the agreement, the sheet that lists instalment numbers and dates, rather than off the conversation at the counter. A tenure discussed and a tenure signed are two different things often enough to be worth the ten seconds.

Input three: the contracted rate

The rate is the input that carries the trap, and the trap is set out in full below. The charge each month is worked out on what is still owed, so the panel computes on the reducing-balance rateA rate charged on what is still owed rather than on what was originally borrowed, so the rupees of charge fall as the debt falls.. The basis field beside the rate exists so that a flat quotation can be handed over honestly rather than typed into the wrong box. The Bhosale household's agreement carries 11.2913 per cent a year on that basis. Rounded to two places that reads as 11.29 per cent, and it works out at about 0.94 per cent a month. The four places matter to the tool and to nothing else: they are what makes the instalment land on Rs 3,150/- to the rupee rather than a rupee either side of it. Field note: read the rate off the rate clause in the agreement or off the schedule of charges, and note that most agreements print two rate figures rather than one.

What comes out, and which output can be compared across two offers?

The instalment is Rs 3,150/- a month: the number the household is quoted, the number that goes into the monthly budget, and the number a lender leads with. The total repayableThe instalment multiplied by the number of months, which is what the borrowing costs in total rather than what it costs in a month. is Rs 3,150/- times thirty, or Rs 94,500/-. Take the Rs 82,000/- back out of that and Rs 12,500/- is left as the charge on the borrowing.

Only one of those two outputs can be compared between two offers, and it is not the instalment. An instalment is a monthly amount and it can be made smaller by stretching the tenure, so on its own it says nothing about cost. The total repayable already contains the tenure inside it. Containing the tenure is exactly what makes it comparable. The tool prints both side by side for that reason and for no other.

Here is the same Rs 82,000/- at the same contracted rate over five tenures, computed by the panel rather than asserted. Nothing else changes across these rows.

Read the two middle columns in opposite directions and the whole relationship is there. Wherever a charge is being made at all, lengthening the tenure moves the instalment down and the total repayable up. The 48 month row is Rs 1,019/- a month easier than the 30 month row and Rs 7,785/- more expensive in total, and the panel's second drive button walks that trade in one press, naming both movements at once on the line under the readouts. Set the rate in the panel to nil and the pairing comes apart. The claim has an honest limit: with nothing being charged the instalment still falls with a longer tenure, but the extra months cost nothing, so the total stops moving. Neither of those facts is a verdict on anything. A household with Rs 2,131/- of room in a month and not Rs 3,150/- is not choosing to pay more; it is choosing the row it can actually stand each month, and that is a different kind of decision from the one a calculator can hold.

What is a single instalment actually made of?

The bank statement shows one line, one amount, thirty times over, the same Rs 3,150/- leaving the account on the 7th. Inside the loan that identical payment is doing two jobs in wildly different proportions depending on which month it is. The charge for a month is the outstanding balanceWhat is still owed on the loan after a given instalment has been paid, before the next month's charge is added. multiplied by the monthly rate, and whatever is left of the instalment after that charge goes to the debt. In the first month the balance is the whole Rs 82,000/-, so the charge is Rs 772/- and Rs 2,378/- reaches the debt. By the thirtieth the balance has fallen to Rs 3,121/-, so the charge is Rs 29/- and Rs 3,121/- reaches the debt. Same payment, and the two parts have almost completely swapped places.

How does the split move across the whole tenure?

Not in a straight line, and this is the finding that makes the schedule worth printing at all. The charge is taken on what is still owed, so it is largest at the start when the balance is largest, and it shrinks every month as the balance shrinks. Across the whole thirty months the charge comes to Rs 12,500/-, and Rs 9,125/- of that Rs 12,500/-, nearly three quarters of it, falls in the first fifteen months. Those same fifteen months clear Rs 38,125/- of the Rs 82,000/-, which is under half, and Rs 9,125/- plus Rs 38,125/- is the Rs 47,250/- of instalments those fifteen months carried.

The consequence turns up in the one place a household actually looks: what is still owed. After fifteen of thirty instalments the balance is not half of Rs 82,000/-. The balance is Rs 43,875/-, or Rs 2,875/- more than half, and Rs 2,875/- is nine tenths of an entire instalment. The balance does not fall below Rs 41,000/- until the seventeenth instalment has been paid. Halfway through the months is not halfway through the debt, and on this loan it is two instalments short of it.

The schedule, at the months worth naming

The panel above prints all thirty rows and adds them up underneath. Ten of those rows carry the whole movement, from the first instalment to the last.

Two checks hold on the full thirty rows and both are worth running on any schedule at all: the charge column adds to Rs 12,500/-, the debt column adds to Rs 82,000/-, and together they make the Rs 94,500/- the panel printed before it printed any row at all. A schedule that does not reconcile in both of those directions has something wrong in it. Finding out takes about a minute. This is the amortisationThe month by month splitting of each instalment into the charge for that month and the part that reduces the debt, until the debt reaches nil. of the loan, which is only a long word for the two columns in the shopkeeper's notebook.

The panel at the top prints all thirty of those rows live and adds both column sums underneath them, so a schedule off any agreement can be rebuilt in it and checked the same way in about a minute.

Where does the reading go wrong most often?

What happens when the same borrowing is quoted the other way?

The mistake above is not that the flat figure exists. The mistake is that a figure was moved between two bases without the basis moving with it, and the panel has a field for exactly that. Set the basis field to flat, leave 6.10 in the rate field, and the panel returns the household's own Rs 3,150/- instalment and its own Rs 94,500/- total, printing beside them the reducing-balance figure that quotation is equivalent to: 11.29 per cent a year. One borrowing, one instalment, one charge of Rs 12,500/-, and two rate numbers, the larger close to double the smaller. A rate figure means nothing until the basis it is quoted on is read with it. The panel prints both quotations of whatever borrowing is in it for that reason, and never lets the pair be separated.

The gap between the two quotations is also what makes the mis-selling work. A borrower holding 6.10 against a competing 11.29 will read the first as roughly half the price of the second, when the two can describe the identical borrowing. Nothing about the arithmetic is hidden. The flat figure is smaller because it is measured against the whole original amount for the whole tenure. The reducing figure is measured against a balance that is falling every month. The check is the same single line either way. Whatever rate is printed, the instalment times the tenure has to reach the total repayable, and the total is the one figure that survives a change of basis unaltered.

What can the arithmetic never settle?

Arithmetic cannot say whether a borrowing is worth taking. Rs 12,500/- to have a two-wheeler thirty months earlier than saving for it would have allowed is a number, and whether that number was worth paying depends on what the two-wheeler carried, who it carried and what the alternative was. None of that is in the amount, the tenure or the rate, so none of it is in the output.

A missed instalment, an early closure or a rate that moves during the tenure each change the schedule, and none of the three is anywhere in an amount, a tenure and a rate. Those three inputs answer exactly one question: what a stated borrowing costs and what each of its instalments is made of. Every other question a household actually has sits outside the arithmetic, and a calculator with opinions would be a worse calculator.

How does a lender use the same schedule?

The lender is running these identical thirty rows on its own systems, and it reads two columns the household rarely sees printed together. The balance column answers what is still owed at any date. A statement of account or a closure quote is built from that figure. The charge column records the lender's earnings for that month, so an interest certificate for a year is a sum of charge rows rather than a sum of instalments.

For a household the same two columns answer two different questions, and knowing which column to look at is most of the skill. The balance column answers what is left to pay. The charge column, added up, answers what the borrowing has cost so far. The total repayable, available on day one, answers what it will have cost in all. A borrowing the household can describe in those three numbers is a borrowing it can plan around, and one it can only describe as Rs 3,150/- on the 7th is not. Field note for both: the balance appears on the lender's statement of account, and the charge for a period appears on the interest certificate or the equivalent statement the lender issues, whatever it is called on the letterhead.

None of this requires the household to be good at arithmetic. The work requires three numbers written down once, on one sheet, where they can be found again. The Bhosale household paid its thirtieth instalment in January of the second year and the borrowing closed on schedule, for reasons that had nothing to do with how the rest of that year went.

The Bhosale household, Meghna Bhosale, Ashok Bhosale, Ira Bhosale and Sahyadri Freight Services Private Limited are invented.
Educational material. Not advice on any investment, tax, budget or market position.