EMI Calculation Formula and Monthly Payment Example

The EMI (equated monthly instalment) formula calculates a fixed monthly loan payment from the principal, annual interest rate and repayment term. Enter those three values to estimate the monthly payment and total interest; the calculation assumes a fixed rate and monthly payments.

Formula

For a fixed-rate loan with equal monthly payments, the standard EMI formula is:

EMI = P × r × (1 + r)ⁿ ÷ [(1 + r)ⁿ − 1]

An equivalent form used by the calculator is EMI = P × r ÷ [1 − (1 + r)⁻ⁿ]. Here:

• P is the principal, or amount borrowed, in your currency.
• r is the monthly interest rate as a decimal. For an annual APR entered as a percentage, r = APR ÷ 1,200. An 8% APR therefore gives a monthly rate of 0.0066667, or about 0.6667%.
• n is the number of monthly payments. With a term in years, n = years × 12.
• EMI is the monthly payment, in the same currency as the principal.

The formula spreads repayment across the term so the monthly payment covers interest due and part of the principal. It is designed for a positive interest rate and a level payment schedule. The displayed payment is rounded to two decimal places; total interest is calculated using that rounded payment multiplied by the number of months, less the original principal.

Worked Example

Using the calculator’s default inputs—loan amount 20,000, APR 8%, and term 5 years—the number of payments is 5 × 12 = 60. The monthly rate is 8 ÷ 1,200 = 0.0066667.

1. Calculate the growth factor: (1 + 0.0066667)⁶⁰ ≈ 1.48985.
2. Substitute into the formula: EMI = 20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰].
3. The unrounded payment is about 405.53, so the monthly EMI rounded to cents is 405.53.
4. Total payments using the rounded instalment are 405.53 × 60 = 24,331.80. Estimated total interest is 24,331.80 − 20,000 = 4,331.80.

Small differences can arise if a lender uses a different day-count convention, payment date, rounding method, or rate definition. The worked example follows the calculator’s stated monthly-rate and cent-rounding assumptions.

Assumptions

• The interest rate remains fixed throughout the repayment term.
• Payments are equal, made monthly, and treated as end-of-month payments.
• Interest is modelled monthly at APR divided by 12.
• The estimate excludes fees, taxes, insurance, PMI and escrow because they are not inputs.

How to Read an EMI Estimate

The monthly EMI is the scheduled principal-and-interest payment under the assumptions above. The total-interest figure is the estimated amount paid above the principal over the full term. It does not include separate charges, and it is not necessarily the same as a lender’s total cost figure.

Principal, rate and term affect the result in different ways. A larger principal raises the payment when other inputs are unchanged. A higher rate also raises the payment and generally increases the interest portion. A longer term usually lowers the monthly instalment for a positive rate, but it means more monthly payments and can increase total interest. These are mathematical effects, not a judgment about whether a loan is suitable.

To make an estimate useful, enter the amount actually being financed, the rate and the repayment term stated in the lender’s documents. If the lender quotes an annual percentage rate that includes charges, the quote may not map exactly to a simple nominal rate divided by 12. Ask how the lender defines the quoted rate and payment schedule.

EMI Compared With Principal and Interest

An EMI is the combined scheduled payment, not the amount of principal repaid each month. In a standard amortizing loan, interest for a month is calculated on the outstanding balance. Early in the schedule, that interest can make up a larger share of the payment; as the balance falls, the interest share generally declines and more of each level payment reduces principal.

For example, at the start of the default example, monthly interest is approximately 20,000 × 0.0066667 = 133.33. From a 405.53 payment, about 272.20 goes toward principal before any lender-specific rounding. In later months, interest is calculated on a smaller balance. The total EMI can remain level even while its principal and interest components change.

Common Errors and Formula Limits

• Using the annual rate as the monthly rate: APR entered as a percentage must be divided by 1,200 to produce a monthly decimal rate. Using 8 instead of 0.0066667 would be a major unit error.
• Mixing years and months: This calculator accepts years and converts them to months. If working by hand with a term in months, use that number directly as n; do not multiply it by 12 again.
• Confusing flat interest with reducing-balance interest: The EMI formula assumes interest accrues on the remaining balance. A flat-rate quotation uses a different calculation and cannot be compared by treating its rate as the same input without clarification.
• Rounding at different stages: Rounding the monthly payment to cents and then multiplying by the number of payments can produce a slightly different total from calculations that retain extra decimals or adjust the final instalment.

This formula is not a complete model for variable-rate loans, irregular payment dates, interest-only periods, balloon payments, skipped instalments, extra principal payments, or loans with fees added to the balance. A changing rate can change the payment or repayment schedule, depending on the contract. The calculator also does not determine eligibility, approval, or a lender’s exact payment amount.

Frequently Asked Questions

How do I calculate EMI manually?
Convert the annual percentage rate to a monthly decimal by dividing by 1,200, convert the term to monthly payments, and substitute the principal, monthly rate and payment count into the EMI formula above.

Does EMI include interest?
Yes. A standard EMI combines principal repayment and interest. It generally does not include separate fees, insurance, taxes or escrow unless the lender explicitly includes them in the quoted payment.

Why does a longer loan term reduce the EMI?
The principal is divided across more scheduled payments, so the calculated monthly amount is generally lower. Interest accrues for longer, however, so total interest may be higher.

Is EMI the same as the total monthly loan cost?
Not always. EMI usually refers to the scheduled loan instalment. Other charges may be billed separately or included in a lender’s payment estimate, so check what the quoted amount covers.

Can this formula calculate a variable-rate EMI?
It can estimate a payment for one rate at a time, but it does not model future rate changes. A changing-rate loan requires the applicable contract rules and updated balance and payment information.

This result is an estimate; the lender’s disclosure gives the exact figures.

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in p | Loan amount | - | 20000 | 1 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in yrs | Loan term | years | 5 | 0.0833 | 50
out pmt | Monthly EMI | - | round(p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)), 2) | 2
out int | Total interest | - | pmt * yrs * 12 - p | 2