How Loan EMI Is Calculated, Step by Step With Examples

A loan EMI, or equated monthly instalment, is the fixed amount you pay every month so that the loan and all its interest are cleared exactly on the last payment. It is calculated with one formula: EMI = P × r × (1 + r)^n ÷ ((1 + r)^n − 1), where P is the amount borrowed, r is the monthly interest rate as a decimal, and n is the number of monthly payments. For 10,000 borrowed at 7.5 per cent a year over five years, the EMI is 200.38.

The figures in this article are estimates, not advice; lenders round differently and add charges that the formula does not know about.

What the formula is really doing

Every month, interest is charged on whatever you still owe. Your payment first covers that month's interest, and the remainder reduces the balance. Next month, interest is charged on the smaller balance, so a little more of the same payment goes towards the principal. The formula simply finds the one payment amount that makes this process land on a balance of exactly zero after n months.

Three inputs drive it:

• P, the principal. The amount actually lent, after any fees deducted up front.
• r, the monthly rate. The annual rate divided by 12 and expressed as a decimal. An annual rate of 7.5 per cent is 7.5 ÷ 12 = 0.625 per cent a month, which is 0.00625.
• n, the number of payments. Years multiplied by 12. Five years is 60 payments.

The expression (1 + r)^n is the growth factor: what one unit of debt would become if nothing were paid for the whole term. Everything else in the formula spreads that growth evenly across the payments.

Why not simply divide the loan plus interest by the number of months? Because the interest is not known until you know the payments, and the payments depend on the interest. Each month's charge depends on the balance left by the previous month, which depends on how much of the previous payment went to principal. The formula resolves that circularity in one step. A spreadsheet can do the same thing by trial and error, nudging the payment up and down until the final balance is zero, and it arrives at exactly the same figure.

The word "equated" in the name is the point: the instalments are equal. A lender could just as easily charge you the actual interest each month plus a fixed slice of principal, and some business loans work that way, but the payments would then start high and fall every month. Borrowers prefer a flat, predictable amount, so the equal-instalment formula became the default for personal loans, car finance and mortgages alike.

A fully worked example

Take a loan of 10,000 at 7.5 per cent a year, repaid over five years.

1. Monthly rate: r = 0.075 ÷ 12 = 0.00625.
2. Number of payments: n = 5 × 12 = 60.
3. Growth factor: (1.00625)^60 = 1.45329 (a calculator with a power key, or a spreadsheet, gives this directly).
4. Numerator: P × r × 1.45329 = 10,000 × 0.00625 × 1.45329 = 90.83.
5. Denominator: 1.45329 − 1 = 0.45329.
6. EMI = 90.83 ÷ 0.45329 = 200.38.

Over 60 months you pay 200.38 × 60 = 12,022.80 in total, of which 10,000 is the loan itself and 2,022.80 is interest. (The exact unrounded figure is a few pence lower, because the payment itself has been rounded to the nearest penny.) The Loan EMI Calculator performs these steps and shows the schedule described next.

The amortisation schedule explained

An amortisation schedule lists every payment and splits it into interest and principal. The payment is constant; the split is not. Here are the first three months of the example, then a sample from later in the term.

Month	Payment	Interest	Principal	Balance after
1	200.38	62.50	137.88	9,862.12
2	200.38	61.64	138.74	9,723.38
3	200.38	60.77	139.61	9,583.77
12	200.38	52.72	147.66	8,287.37
24	200.38	41.26	159.12	6,441.78
36	200.38	28.90	171.48	4,452.92
48	200.38	15.59	184.79	2,309.65
60	200.38	1.24	199.13	0.00

Month 1 is the easy one to check by hand. Interest is 10,000 × 0.00625 = 62.50. The rest of the payment, 200.38 − 62.50 = 137.88, reduces the balance to 9,862.12. Month 2 charges interest on that: 9,862.12 × 0.00625 = 61.64, leaving 138.74 for principal. Each month the interest portion shrinks by a little under one unit and the principal portion grows by the same amount.

Two things follow from the shape of this table. First, after a year you have paid 2,404.56 but only cut the balance by 1,712.63; the rest was interest. Second, prepaying early is worth far more than prepaying late, because the early balance is what generates most of the interest.

How rate and tenure change the total

The interest rate changes the cost in the way you would expect. The tenure is the one people underestimate. Both tables use the same 10,000 loan.

Annual rate (5 years)	EMI	Total paid	Total interest
5.0%	188.71	11,322.74	1,322.74
6.0%	193.33	11,599.68	1,599.68
7.5%	200.38	12,022.77	2,022.77
9.0%	207.58	12,455.01	2,455.01
12.0%	222.44	13,346.67	3,346.67

Tenure (at 7.5%)	EMI	Total paid	Total interest
1 year	867.57	10,410.89	410.89
2 years	450.00	10,799.90	799.90
3 years	311.06	11,198.24	1,198.24
5 years	200.38	12,022.77	2,022.77
7 years	153.38	12,884.15	2,884.15
10 years	118.70	14,244.21	4,244.21

Read the second table from the bottom. Stretching the loan from five years to ten cuts the payment from 200.38 to 118.70, a 41 per cent drop, but the interest bill more than doubles, from 2,022.77 to 4,244.21. Going the other way, from five years to three, raises the payment by 55 per cent and saves 824.53. A longer tenure is not wrong if the lower payment is what keeps the budget safe, but it should be a deliberate choice, not a default. The Percentage Calculator is handy for working out those percentage changes when you compare two offers.

Reducing balance versus flat rate

Everything above assumes a reducing-balance loan: interest is charged on the outstanding balance, which falls every month. Some personal loans, car finance deals and informal lenders quote a flat rate instead, where interest is charged on the original amount for the whole term. The two numbers are not comparable, and the difference is large.

Flat-rate interest is simple interest on the original amount, so the Simple Interest Calculator reproduces the 3,750 above if you enter 10,000, 7.5 per cent and five years. A rough rule: a flat rate is equivalent to a reducing-balance rate of about 1.8 times as much on a five-year loan, and the multiple grows with the term. Always ask which method a quoted rate uses, and ask for the annual percentage rate (APR), which by law in most countries must reflect the true reducing-balance cost including compulsory fees.

What prepayment does

Paying extra straight off the principal shortens the loan or lowers the payment, depending on what the lender allows. The sooner you do it, the more interest it removes, because the removed balance would otherwise have been charged interest for every remaining month.

Lenders usually offer two ways to apply a lump sum. Reduce the tenure keeps the payment at 200.38 and finishes earlier, which is what the example above shows and which saves the most interest. Reduce the EMI keeps the original end date and lowers the monthly amount instead; it eases the budget but leaves the balance outstanding for longer, so the saving is smaller. If you can keep paying the same amount, choose the shorter tenure.

Before prepaying, check three things: whether the lender charges a prepayment penalty (common on fixed-rate loans, often 1 to 3 per cent of the amount prepaid), whether the extra will shorten the term or reduce the EMI (shortening saves more), and whether the money would be better placed clearing a more expensive debt such as a credit card first. The Credit Card Payoff Calculator shows how long a card balance takes to clear at a given monthly payment and how much interest it costs, which makes that comparison concrete.

Why your lender's figure may differ slightly

If a bank quotes 200.41 or 200.35 for the loan in the example, the formula is not wrong; the lender is using a slightly different convention. The common causes are worth knowing so you can tell a rounding difference from a hidden charge.

• Daily interest. Many banks accrue interest daily on the balance and collect it monthly. Months of 28, 30 and 31 days then produce small variations in each instalment, and the EMI shown on the agreement is an average.
• Payment timing. The standard formula assumes each payment arrives at the end of its month. If the first instalment is due on the day the loan is paid out, which some car finance agreements require, the whole schedule shifts by one month and the payment falls slightly.
• A broken first period. A loan paid out on the 20th with instalments due on the 1st has an odd first period. Lenders either charge interest for those days separately or fold it into the first EMI.
• Rounding. Some lenders round the EMI up to the nearest whole unit and make the final payment smaller to compensate.

Any of these moves the payment by a few pence or a few units at most. A gap of more than that between your calculation and the quote means something has been added to the principal, and the next section lists the usual suspects.

What lenders add on top

The formula gives the cost of borrowing the money. The price of the loan is often higher.

• Processing or arrangement fees. Typically 0.5 to 2 per cent of the principal, either paid up front or deducted from the amount you receive. A 1 per cent fee on 10,000 means you get 9,900 but repay as if you borrowed 10,000, which quietly raises the effective rate.
• Loan insurance. Payment protection or credit life cover, sometimes presented as compulsory. It can add several per cent to the total and is usually optional in law even when the sales script implies otherwise.
• Late payment charges. A fixed fee plus penalty interest on the overdue amount. One missed payment can cost more than a month's interest.
• Prepayment or foreclosure charges. As above; check before signing if you expect to clear the loan early.
• Rate type. A floating rate changes the EMI or the tenure when the lender's base rate moves, so the schedule you calculate today is a starting point, not a promise.

The honest comparison between two offers is the total amount repaid over the term including every compulsory charge, or the APR, which packages the same information as a single rate. Two loans with the same 7.5 per cent headline can differ by hundreds once fees are included.

Where to go next

Put your own figures into the Loan EMI Calculator to see the payment, the total interest and the full month-by-month schedule, then change the tenure by a year in each direction and watch what happens to the interest column. If the loan is for a home, the Mortgage Calculator adds the costs that sit outside the formula. Both run in your browser and store nothing.

Frequently asked questions

What is the formula for EMI?

EMI = P × r × (1 + r)^n ÷ ((1 + r)^n − 1). P is the amount borrowed, r is the monthly interest rate as a decimal (the annual rate divided by 12 and then by 100), and n is the total number of monthly payments. For 10,000 at 7.5 per cent over five years, r is 0.00625 and n is 60, which gives an EMI of 200.38. Spreadsheets provide the same result through the PMT function.

Why is most of my early EMI going to interest?

Interest is charged each month on the balance still owed, and at the start that balance is the whole loan. On a 10,000 loan at 7.5 per cent, the first month's interest is 62.50 and only 137.88 of the 200.38 payment reduces the debt. As the balance falls, the interest portion falls with it and the principal portion grows, until the last payment is almost entirely principal.

Is a longer loan tenure cheaper?

It is cheaper per month and more expensive overall. Stretching 10,000 at 7.5 per cent from five years to ten reduces the payment from 200.38 to 118.70 but raises total interest from about 2,023 to about 4,244. A longer term is sensible when the lower payment protects your monthly budget, but if you can afford the shorter term comfortably it saves a substantial amount of interest.

What is the difference between a flat rate and a reducing balance rate?

A reducing-balance rate charges interest only on what you still owe, which falls every month. A flat rate charges interest on the original amount for the entire term, even after most of it has been repaid. A flat 7.5 per cent over five years costs 3,750 in interest on 10,000, while a reducing-balance 7.5 per cent costs about 2,023. Compare loans on APR, which always uses the reducing-balance method.

Does prepaying a loan reduce the interest?

Yes, and the earlier the better. An extra payment goes straight to the principal, so every later month charges interest on a smaller balance. In the 10,000 example, an extra 1,000 paid after month 12 clears the loan six months early and saves about 325 in interest; the same amount paid after month 48 saves under 100. Check for prepayment penalties before you do it.