The EMI Formula Worked Out by Hand, With a Spreadsheet Version
By Akmal Ali · Published · Updated · 5 min read
EMI = P × r × (1 + r)ⁿ ÷ ((1 + r)ⁿ − 1), where P is the loan amount, r the yearly rate ÷ 12 ÷ 100, and n the number of months. For 20,000 at 12% a year over 3 years, r is 0.01 and n is 36, which gives an EMI of 664.29 and total interest of 3,914.30.
EMI stands for equated monthly instalment: the same payment every month until a loan is repaid. Home loans, car loans and personal loans are usually quoted this way. Knowing how the EMI is calculated helps you compare offers, see what a loan really costs, and understand why the balance falls so slowly at first.
The three inputs
- Principal (P): the amount you borrow.
- Interest rate: the yearly rate the lender quotes. The formula uses the monthly rate, r = yearly rate ÷ 12 ÷ 100. At 10% a year, r = 10 ÷ 12 ÷ 100 = 0.008333.
- Tenure (n): the length of the loan in months. Five years is 60 months.
The EMI formula
EMI = P × r × (1 + r)n ÷ ((1 + r)n − 1)
This is the standard formula for a loan with a fixed rate charged on the reducing balance. That means each month’s interest is charged only on what you still owe. If the rate is 0%, the formula doesn’t apply and the EMI is simply P ÷ n.
Once you have the EMI, two more figures follow:
total repayment = EMI × n
total interest = total repayment − P
Worked example: 100,000 at 10% for 1 year
- Monthly rate: r = 10 ÷ 12 ÷ 100 = 0.0083333.
- Growth factor: (1 + r)12 = 1.008333312 = 1.1047131.
- Top of the fraction: 100,000 × 0.0083333 × 1.1047131 = 920.5942.
- Bottom of the fraction: 1.1047131 − 1 = 0.1047131.
- EMI: 920.5942 ÷ 0.1047131 = 8,791.5887, or 8,791.59 a month.
Over 12 months you repay 8,791.5887 × 12 = 105,499.06, so the total interest is 5,499.06. Twelve payments of the rounded 8,791.59 would come to 105,499.08; lenders often absorb that difference of a few cents in the last instalment. Keep all the decimals until the last step: rounding r or the growth factor too early can change the EMI by a noticeable amount on larger loans.
The amounts in this guide are in no particular currency. The formula works the same for any.
Where does each EMI payment go?
Every EMI is the same, but the split between interest and principal changes. Interest for a month is the balance × r, and the rest of the payment reduces the balance:
| Month | Interest | Principal | Balance after payment |
|---|---|---|---|
| 1 | 833.33 | 7,958.26 | 92,041.74 |
| 2 | 767.01 | 8,024.57 | 84,017.17 |
| 3 | 700.14 | 8,091.45 | 75,925.72 |
| 12 | 72.66 | 8,718.93 | 0.00 |
Early payments are mostly interest, later ones mostly principal. On long loans the effect is much stronger, which is why paying extra early on saves the most interest.
EMI Calculator
Enter the amount, rate and term to get the EMI, total interest and a year-by-year breakdown, in any currency.
More examples
| Loan | Rate | Tenure | EMI | Total interest |
|---|---|---|---|---|
| 20,000 | 12% | 3 years | 664.29 | 3,914.30 |
| 500,000 | 9% | 5 years | 10,379.18 | 122,750.66 |
| 3,000,000 | 8.5% | 20 years | 26,034.70 | 3,248,327.28 |
How do the rate and tenure change the cost?
Take the 3,000,000 loan at 8.5% over 20 years, and change one thing at a time:
| Change | EMI | Total interest |
|---|---|---|
| 15 years instead of 20 | 29,542.19 | 2,317,593.61 |
| 20 years (base case) | 26,034.70 | 3,248,327.28 |
| 25 years instead of 20 | 24,156.81 | 4,247,043.75 |
| 7.5% instead of 8.5% | 24,167.80 | 2,800,270.99 |
| 9.5% instead of 8.5% | 27,963.94 | 3,711,344.55 |
Stretching the loan from 20 to 25 years lowers the EMI by less than 1,900 but adds almost a million in interest. One percentage point on the rate changes the total interest by roughly 450,000 either way. When you compare offers, look at the total interest, not just the monthly payment.
Is a flat rate cheaper than a reducing-balance rate?
Some lenders quote a flat rate, where interest is charged on the full original amount for the whole term. It looks cheaper than it is. On 500,000 at a flat 9% for 5 years, the interest is 500,000 × 9% × 5 = 225,000, and the monthly payment is 725,000 ÷ 60 = 12,083.33. At a 9% reducing-balance rate, the same loan costs 10,379.18 a month and 122,750.66 in interest. Put the other way, a flat 9% costs the same as a reducing-balance rate of about 15.7%. Always ask which method an offer uses.
Calculating EMI in a spreadsheet
Excel, Google Sheets and LibreOffice have a built-in function for the same formula:
=PMT(8.5%/12, 240, -3000000)The first value is the monthly rate, the second the number of months, and the loan amount is entered as negative so the result is positive. This returns 26,034.70, the same as the formula.
Why doesn’t the lender’s EMI match the formula?
Lenders may charge processing fees or insurance, calculate interest daily, round each payment, or start with a partial first month. Their EMI can therefore differ slightly from the formula. Use the formula and the EMI calculator to compare offers on equal terms, and ask the lender for a full repayment schedule before you sign. These figures are estimates, not financial advice.
Interest on savings works in the opposite direction, growing over time. To see how, read how compound interest works, or try the compound interest calculator.
Frequently Asked Questions
How much can I borrow for a given EMI?
Rearrange the formula: P = EMI × ((1 + r)ⁿ − 1) ÷ (r × (1 + r)ⁿ). At 10% a year over 12 months, an EMI of 5,000 supports a loan of about 56,872.54.
Can my EMI change during the loan?
Not on a fixed-rate loan. On a floating-rate loan, when the rate changes the lender either changes the EMI or keeps it and changes the number of months, so ask which one your lender does.
What happens during an EMI holiday or moratorium?
You pay nothing, or only interest, for a while. Interest usually keeps building up on the balance, so afterwards the EMI is higher or the loan runs for longer. Ask the lender for the new schedule before you agree.
Does paying extra reduce the total interest?
Usually, because it lowers the balance that interest is charged on. The effect is largest early in the loan. Check whether your lender charges a fee for prepayment first.