EMI Calculator Equation: Formula and Worked Example

The EMI calculator equation finds the fixed monthly instalment needed to repay a loan over a set term at a fixed annual interest rate. Enter the principal, APR and term to estimate the monthly payment and total interest, in your currency.

Formula

For a fixed-rate, fully amortizing loan with monthly payments, the EMI (equated monthly instalment) is:

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

An equivalent form is EMI = P × r ÷ [1 − (1 + r)⁻ⁿ]. The calculator rounds the payment to two decimal places in your currency. Its monthly rate is the annual percentage rate divided by 12 and by 100.

• P is the amount borrowed, in your currency.
• r is the monthly interest rate as a decimal: APR ÷ 1200.
• n is the number of monthly payments: loan term in years × 12.
• EMI is the fixed monthly instalment, in your currency.

Total interest in this calculator is monthly EMI multiplied by the number of payments, minus the original principal. Because each instalment is rounded to the nearest cent (or equivalent currency unit), the final payment in a real repayment schedule may need a small adjustment.

Worked Example

Using the calculator’s default values—principal of 20,000, APR of 8%, and a five-year term—in your currency:

1. Convert APR to a monthly decimal rate: 8 ÷ 1200 = 0.0066666667.
2. Convert the term to payments: 5 × 12 = 60 months.
3. Substitute into the equation: EMI = 20,000 × 0.0066666667 ÷ [1 − (1 + 0.0066666667)⁻⁶⁰].
4. The unrounded instalment is about 405.5277; rounded to two decimal places, the monthly EMI is 405.53.
5. Total payments using the rounded EMI are 405.53 × 60 = 24,331.80. Subtract the principal: 24,331.80 − 20,000 = 4,331.80 total interest.

The figures are expressed in your currency because the formula works the same way regardless of the currency unit. For an actual estimate, use the principal, APR and term supplied for the loan you are examining.

Assumptions

• The interest rate stays fixed throughout the modeled term.
• Payments are equal monthly instalments, made at the end of each monthly period.
• Interest is compounded monthly using APR ÷ 12; the APR is entered as a percentage per year.
• The estimate excludes fees, taxes, insurance, PMI and escrow. It assumes these are not added to the principal or instalment.

How EMI Works

An EMI combines interest and principal in one regular payment. Early in a conventional amortizing loan, the outstanding balance is relatively large, so more of the payment goes toward interest. As the balance falls, the interest portion generally shrinks and a larger portion of each fixed payment reduces principal. If the stated rate and payment schedule remain unchanged, the payment amount stays level even as its components change.

The equation is derived by discounting each of the n equal payments at the monthly rate r. Their present values must add up to the amount borrowed. Solving that relationship for the payment produces the EMI formula. It is therefore not simply principal divided by the number of months: that shortcut omits interest.

EMI is commonly used to describe scheduled monthly repayments on loans. The underlying calculation is not tied to a particular loan category; it applies when the balance is repaid through equal periodic payments at a fixed rate. A variable rate, irregular payments, or a payment holiday changes the schedule and may change the amount due.

Using the Result and Checking Inputs

The first result is the estimated monthly instalment. The second is the interest paid over the modeled term, calculated from the rounded instalment. Together they help show the payment size and the aggregate interest implied by those assumptions; neither figure includes charges not entered into the calculation.

Check the lender’s figures before comparing a calculator estimate with a quoted payment. Differences can come from a different APR, term, payment date, financed fees, rounding method, or a first period that is longer or shorter than a full month. The calculator uses APR as a nominal annual rate divided into 12 monthly periods. A quoted effective annual rate may need conversion before it matches this convention.

• Enter the amount borrowed, not an unrelated purchase price, unless the full purchase price is actually financed.
• Enter APR as a percentage, such as 8 for 8%, not as 0.08.
• Enter the term in years. The equation converts it to months by multiplying by 12.
• Keep currency units consistent. Changing from one currency to another does not change the arithmetic, but the inputs and outputs must use the same unit.
• Do not interpret total interest as the total cost of borrowing when fees or other charges apply.

Limits and Common Misconceptions

A fixed EMI does not mean the same amount of principal is repaid each month. The interest share changes as the balance changes. Nor does the result show whether a lender will approve a particular loan or what payment will appear in a lender’s final schedule; those depend on information and terms not represented by these three inputs.

This equation also assumes a positive APR and a regular monthly schedule. At a zero interest rate, the limiting calculation is principal divided by the number of payments, but this calculator requires a minimum APR of 0.01% because its displayed formula uses the positive-rate form. For a rate-changing loan, the fixed-rate equation can estimate a period only if the rate and repayment assumptions for that period are explicitly specified; it does not forecast future adjustments.

Rounding matters over many payments. The calculator rounds each modeled EMI to two decimal places and uses that rounded payment to calculate total interest. A lender may instead calculate interest daily, use different payment timing, or adjust a final instalment to clear a small remaining balance. Treat the result as an estimate; the lender’s disclosure gives the exact figures.

Frequently Asked Questions

What does EMI stand for?
EMI stands for equated monthly instalment: a scheduled monthly payment that combines principal repayment and interest under the stated assumptions.

How do I calculate EMI by hand?
Convert the annual percentage rate to a monthly decimal by dividing it by 1200, convert the term to months, then substitute the principal, monthly rate and payment count into the EMI equation above.

Is EMI the same as principal divided by the number of months?
No. Principal divided by months ignores interest. The EMI equation includes the monthly interest rate and calculates a level payment that covers interest and repays the balance over the term.

Why is the interest portion higher at the start?
Interest for a period is based on the outstanding balance. That balance is largest near the start of repayment, so more of a level payment goes to interest then; as principal is repaid, the interest portion generally declines.

Does the EMI include fees and insurance?
Not in this calculator. It uses only the loan amount, APR and term. Fees, insurance, taxes, PMI and escrow are excluded unless they are incorporated into the loan amount or modeled separately.

Can I use this equation for a variable-rate loan?
It can calculate a payment for a specified rate and term, but it does not model future rate changes. If the rate changes, the payment or repayment period may also change under the applicable loan terms.

Related

• Housing Loan EMI Calculator: Formula and Worked Example
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• Business Loan EMI Calculator and Payment Formula

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