Unyfy logoUnyfy
    Back to all articles

    EMI calculation formula, worked by hand on one loan

    The EMI calculation formula produces one number, and the number hides the part that matters. Every EMI is the same size, but each one buys something different. On an illustrative ₹5 lakh loan at 13 percent over 48 months, the first ₹13,414 instalment sends ₹5,417 to interest; the last sends ₹144. The first year is a quarter of the loan's life and carries 41.1 percent of all the interest it will ever charge. That one pattern decides when a part-payment is worth making, whether to cut the EMI or the tenure afterwards, and why a loan refinanced late saves almost nothing.

    This page works the formula by hand, so you can check any lender's figure with a phone calculator and a pencil. Then the schedule's first six rows and its last, the interest charged for the odd days before your first EMI, and a ₹1 lakh part-payment after EMI 12 worked both ways. Kept at the same EMI, it saves ₹39,990 and closes the loan ten instalments early. Kept at the same tenure, it saves ₹21,304 and lowers the EMI by ₹3,369.

    Every figure below comes from the same loan, so each step can be checked against the one before it. Swap in your own principal, rate and tenure and the method carries over unchanged.

    EMI calculation formula, worked by hand

    The technique

    Everything goes in as a monthly number

    The formula is exact; the mistakes come from feeding it annual inputs. The rate enters as a monthly decimal, so 13 percent a year becomes 0.010833, and the tenure as a count of instalments, 48 rather than 4. Enter the annual rate or the tenure in years and the result is not slightly off, it is meaningless, which is why a hand check sometimes seems to prove the lender wrong when it is the check that is wrong.

    The formula is E = P × r × (1+r)^n ÷ ((1+r)^n − 1). P is the principal, r the monthly rate as a decimal (the annual percentage divided by 12, then by 100), and n the number of monthly instalments. It is the reducing balance EMI formula: it assumes each month's interest is charged only on what is still owed, and solves for the one fixed payment that brings the balance to zero after exactly n months.

    The only awkward step is raising 1.010833 to the 48th power. A phone calculator without a power key can still do it by squaring: square once for the 2nd power, square that for the 4th, again for the 8th, the 16th and the 32nd, then multiply the 32nd by the 16th to reach the 48th. Keep four decimal places at every step; rounding earlier drifts the answer by a few rupees. Here is the whole EMI calculation example on the loan used throughout.

    ₹5 lakh, 13 percent, 48 months, by hand
    Monthly rate r = 13 ÷ 12 ÷ 100
    0.010833
    (1+r) squared, then the 4th and 8th powers
    1.0218, 1.044, 1.09
    16th and 32nd powers
    1.1882, 1.4117
    48th power = 32nd × 16th
    1.6773
    P × r = ₹5,00,000 × 0.010833
    ₹5,416.67
    Numerator: ₹5,416.67 × 1.6773
    ₹9,085.54
    Denominator: 1.6773 − 1
    0.6773
    EMI: ₹9,085.54 ÷ 0.6773, rounded to the rupee
    ₹13,414

    Unrounded, the EMI is ₹13,413.75. The loan and its 13 percent rate are illustrative; a sanctioned rate depends on the lender and your profile.

    • ₹13,414 × 48 is ₹6,43,872, so the formula says the loan costs ₹1,43,872 in interest. The schedule below charges ₹1,43,858, because the final EMI is trimmed to ₹13,400 to land the balance exactly on zero
    • P × r is the first month's interest, ₹5,417 here. If your lender's first row shows something different, it is almost certainly counting days rather than months, which the next section explains

    EMI calculation methods and why lenders differ

    There are three ways to reach the same EMI, and it is worth knowing all three because each checks a different thing. The formula gives the instalment. A spreadsheet's PMT function gives it without the arithmetic. Walking the schedule row by row, interest as balance × r and principal as EMI minus interest, checks that the instalment actually clears the loan. If the three agree and your lender's number does not, the difference has one of a few causes.

    The common one is daily interest. Many lenders charge interest on the actual days in each month at the annual rate ÷ 365, not at a flat twelfth. On ₹5 lakh at 13 percent, a 31-day month then costs ₹5,521 instead of ₹5,417, and a 28-day month ₹4,986. Across a whole year the days add up to the same annual rate, and the EMI is usually still set by the formula, but no single row of a daily-interest schedule will match a monthly one to the rupee. The second cause is EMI in advance, used in some vehicle and equipment finance: the first instalment is collected at disbursal, so the formula is divided by (1+r) and the EMI comes out ₹144 lower. The third is rounding. Some lenders round the EMI up to the next rupee or ten and let the last instalment absorb the difference.

    A flat-rate quote is a different method altogether, not a variant of these; the types of interest rates post converts one to the other. To run your own numbers without the arithmetic, the EMI calculator at /calculator uses this same formula.

    MethodHowEMI on ₹5 lakh, 13%, 48 months
    Formula by handP × r × (1+r)^n ÷ ((1+r)^n − 1)₹13,413.75
    Spreadsheet=PMT(13%/12, 48, -500000)₹13,413.75
    Schedule walkInterest = balance × r, repeated 48 times₹13,414, final EMI ₹13,400
    EMI in advanceFormula ÷ (1+r), first EMI paid on day one₹13,270
    The spreadsheet takes the principal as a negative number because it is money you receive. Daily-interest schedules use the same EMI with slightly different interest in each row.

    Reducing balance EMI formula, row by row

    The amortisation schedule is the formula unrolled. Each row takes the balance left after the previous EMI, charges one month's interest on it, and sends the rest of the ₹13,414 to principal. Because the balance falls, next month's interest is a little smaller, so a little more goes to principal, and so on for 48 rows. Lenders share a Key Facts Statement before you sign, which sets out the repayment schedule along with the all-in cost. Check its first row against P × r before anything else.

    EMI no.EMIInterestPrincipalBalance afterInterest share
    1₹13,414₹5,417₹7,997₹4,92,00340.4%
    2₹13,414₹5,330₹8,084₹4,83,91939.7%
    3₹13,414₹5,242₹8,172₹4,75,74739.1%
    4₹13,414₹5,154₹8,260₹4,67,48738.4%
    5₹13,414₹5,064₹8,350₹4,59,13737.8%
    6₹13,414₹4,974₹8,440₹4,50,69737.1%
    48₹13,400₹144₹13,256₹01.1%
    Monthly interest at 13 ÷ 12 percent on the opening balance, rounded to the rupee each month. The final EMI is adjusted so the balance ends at zero.
    • Between EMI 1 and EMI 6, interest falls by ₹443 and principal rises by exactly ₹443. The EMI never changes; only the split does
    • Each month's principal is about 1.0109 times the last, which is 1 + r. That is the whole engine of the schedule: principal grows at the loan's own monthly rate
    • After 12 EMIs the balance is ₹3,98,102. A quarter of the tenure has passed and 20.4 percent of the principal has been repaid, which is why the outstanding figure in the first year always looks higher than people expect

    Why the interest share is front-loaded

    The technique

    Interest is charged on what you still owe

    A common belief is that lenders collect their interest first, as a policy. Nothing in the formula does that. Each month's interest is the balance times r, and the balance is largest at the start. A fixed EMI therefore has less left over for principal early and more later. The front-loading is arithmetic, and it is also why closing early never means paying interest for months you did not borrow.

    On this loan, the first 12 EMIs pay ₹59,070 of interest and ₹1,01,898 of principal. The last 12 pay ₹10,784 of interest and ₹1,50,170 of principal. The first year carries 41.1 percent of the total interest and the last year 7.5 percent. By the end of month 24, halfway through the tenure, you have paid ₹3,21,936 in EMIs, 72.3 percent of all the interest is behind you, and ₹2,82,140 is still owed: 56.4 percent of what you borrowed.

    A longer tenure sharpens the pattern. Stretch the same ₹5 lakh at 13 percent to 84 months and the EMI falls to ₹9,096, but 59.6 percent of the first EMI is interest, principal only overtakes interest at EMI 21, and the first year repays just 9.4 percent of the loan. Total interest rises to ₹2,64,063. On the 48-month loan, principal exceeds interest from the very first EMI.

    • A rupee prepaid early stops interest for every month that remains. A rupee prepaid in the last year stops interest for a few months only. That is the entire case for early part-payment, and the next two sections put rupees on it
    • Refinancing late rarely pays. After 36 EMIs only ₹10,784 of interest is left on this loan, so a switch that costs a processing fee has almost nothing to save; the question of whether your loan is overpriced is worth asking in year one, not year three
    • The outstanding balance, not the EMI, is what a lender quotes when you ask to foreclose. Read it off the schedule's balance column for the month you plan to close

    Broken-period interest before the first EMI

    The technique

    The odd days before your EMI cycle starts

    Loans run on a fixed EMI date, and money rarely arrives on it. The days between disbursal and the start of the first full EMI period are charged interest separately, outside the formula. People meet it as a first EMI that is larger than promised, or a credit that is smaller than the sanctioned amount, and assume a hidden fee.

    Suppose the ₹5 lakh is disbursed on the 12th and the EMI date is the 5th. The first full period runs from the 5th of the next month, so the 24 days from the 12th to that 5th sit outside the schedule. Broken-period interest is the principal × the annual rate × the days ÷ 365: ₹5,00,000 × 0.13 × 24 ÷ 365 = ₹4,274. Lenders collect it in one of two ways. Some deduct it from the disbursal, so ₹4,95,726 reaches your account. Others add it to the first EMI, which then comes to ₹17,688. Some lenders set the first EMI date so that there is no broken period at all.

    It is not a fee. It is interest at the loan rate for days you actually held the money, ₹178.08 a day here. It is also 0.85 percent of the principal, large enough to notice, so ask for the amount and the method in writing before you sign. Interest should run from the day the money reaches your account, not from the sanction date; if the days are counted from earlier, ask why.

    Broken-period interest on ₹5 lakh at 13 percent, EMI date the 5th
    Disbursed on the 28th: 8 days
    ₹1,425
    Disbursed on the 12th: 24 days
    ₹4,274
    Disbursed on the 6th: 30 days
    ₹5,342
    Difference, 6th against 28th
    ₹3,917

    Actual days ÷ 365. Lenders differ on day count and on whether the amount is deducted from the disbursal or added to the first EMI; your sanction letter says which.

    • If you can choose the disbursal day, taking the money just before the EMI date keeps the broken period short. Disbursal on the 6th costs ₹3,917 more than on the 28th, for 22 more days of money
    • When the interest is deducted, the ₹4,95,726 credit is not a short payment. Match it against the broken-period line in your documents before raising a complaint

    Part-payment at month 12: cut tenure or cut EMI

    After EMI 12 the balance is ₹3,98,102. Pay ₹1,00,000 against it and ₹2,98,102 remains. Without the part-payment, months 13 to 48 would charge ₹84,788 of interest. What happens next depends on one choice the lender will ask you to make, or will make for you if you do not specify it.

    Keep the EMI at ₹13,414 and the tenure shrinks. The months left come from the formula turned around: n = −ln(1 − B × r ÷ E) ÷ ln(1+r), which gives 25.56 on a balance of ₹2,98,102, so 26 more EMIs with a final one of ₹7,550. The loan closes at month 38, ten instalments early, and interest from month 13 falls to ₹44,798: a saving of ₹39,990.

    Keep the tenure at 36 remaining months and the EMI shrinks. The formula on ₹2,98,102 over 36 months gives ₹10,044.23, rounded up to ₹10,045, which is ₹3,369 lower. Interest from month 13 is ₹63,484, a saving of ₹21,304. Cutting tenure saves ₹18,686 more, because the principal left falls faster when the EMI stays high.

    From month 13No part-paymentKeep EMI, cut tenureKeep tenure, cut EMI
    EMI₹13,414₹13,414₹10,045
    EMIs left362636
    Loan closes atMonth 48Month 38Month 48
    Interest, month 13 on₹84,788₹44,798₹63,484
    Interest saved₹39,990₹21,304
    Total paid from month 13, incl. part-payment₹4,82,890₹4,42,900₹4,61,586
    ₹1,00,000 paid immediately after EMI 12 on the illustrative ₹5 lakh, 13 percent, 48-month loan. No part-payment charge assumed here; charges are priced in the next section.
    • Per rupee prepaid, cutting tenure saves 40.0 percent of the part-payment in interest and cutting the EMI saves 21.3 percent. If the goal is total cost, keep the EMI
    • Cutting the EMI is the right call when the monthly outflow is the problem: if EMIs are crowding your income, ₹3,369 of room every month for three years can matter more than ₹18,686 spread over the same three years
    • Put your choice in the part-payment request itself. A lender's default can be either, and the difference here is ₹18,686

    Loan prepayment strategy: when, how, whether

    The technique

    A prepaid rupee earns the loan rate for as long as it would have stayed

    Part-payment strategies are usually argued as habits: prepay every bonus, round up every EMI. The arithmetic is simpler. Each rupee prepaid removes the loan rate on itself for every remaining month, so what it saves depends on how early it goes in, what the lender charges to take it, and what the same rupee would have earned elsewhere.

    Timing first. The same ₹1 lakh, with the EMI kept unchanged, saves ₹39,990 when paid after EMI 12, ₹23,830 after EMI 24 (the loan then closes 15 months later), and ₹9,452 after EMI 36, when the loan closes four EMIs later with a final instalment of ₹11,260. Month 12 beats month 36 by ₹30,538 on identical money.

    Lump sum or spread out? Paying ₹2,778 a month over and above the EMI from month 13, the same ₹1 lakh split across 36 months, closes the loan at month 41 and saves ₹17,439. The lump after EMI 12 saves ₹22,551 more, because all of it stops accruing interest at once. If you are holding money for a part-payment, paying it in sooner beats waiting to collect a round figure.

    Then the charge. Some loans charge for part-payment, commonly fixed-rate ones; whether yours can is set by its terms and by RBI's rules, and the RBI prepayment charges page covers which loans are now exempt. At an illustrative 3 percent plus 18 percent GST, a charge on ₹1 lakh is ₹3,540. After EMI 12 that still leaves ₹36,450 saved if you cut tenure and ₹17,764 if you cut the EMI. After EMI 36 it leaves ₹5,912.

    Finally, the alternative. The same ₹1 lakh in a fixed deposit at an illustrative 7 percent, compounded quarterly for the 36 months, earns ₹23,144 before tax and ₹16,201 after tax at a 30 percent slab. Prepaying saves ₹39,990, which is ₹23,789 more than the deposit after tax. The gap exists because the loan costs 6 points more than the deposit pays, and a saving on a loan is not taxed.

    • Prepay only from money that is genuinely spare. A part-payment cannot be drawn back, so an emergency fund used to prepay turns the next emergency into a new loan at a higher rate
    • Prepay the most expensive debt first. A card balance or a pricier loan should go before a 13 percent personal loan, and the order is decided by rate, not by which loan feels largest
    • Ask the lender for the revised schedule after every part-payment and check the first new row against the new balance × r, as in the section on the formula

    How Unyfy helps with loans you already repay

    Two things on this page depend on facts about your own loans that people rarely have in one place: what every EMI is and when it leaves, and whether a loan's rate is still a fair one for you. Unyfy covers both from your transactions. On Pro, its Fixed Expenses screen predicts what the coming month is already committed to, each EMI named from the lender on the debit with its amount and usual payment days, alongside SIPs, rent and bills on a cycle. And it flags a loan priced above what the same borrower would be offered today, and says whether switching is worth it after the fee, which is the year-one question the front-loading section argues for. It also computes a blended rate across your loans and cards, a single figure to set against the rate of the loan you are thinking of part-paying.

    It reads bank and card transaction emails and, on Android, transactional SMS, with no manual entry. Take the outstanding principal, the broken-period interest and the part-payment terms from your loan statement and sanction letter, and make a part-payment through your lender. It never asks for your bank password or UPI PIN, and every payment is one you authorise. Install Unyfy on Android, or use the web app at app.unyfy.co.in on an iPhone.

    The EMI formula gives one fixed number, ₹13,414 on the ₹5 lakh loan here, and the schedule shows what it buys: interest first because the balance is largest first, with 41.1 percent of all interest paid in the first year. Check your lender's first row against P × r, ask how broken-period interest is charged, and if you part-pay, do it early and keep the EMI unchanged unless the monthly outflow is the problem. After EMI 12, ₹1 lakh saves ₹39,990 that way and ₹21,304 the other way.

    Informational page, not financial advice. The loan, rates, charges and deposit figures on this page are illustrative. Interest methods, day counts, broken-period treatment and part-payment terms differ by lender and by loan; your sanction letter and loan agreement govern, not this page.

    Questions people ask

    Related guides

    Personal loan interest rates: what the number actually means RBI prepayment charges rule 2026: who it frees, who still pays Am I overpaying on my personal loan? Find your real rate first Personal loan guide India: the life of a loan, from need to NOC Compare personal loans: the table lenders do not publish How much of your income can safely go to debt?