Finance & Money

How to Calculate Loan EMI Step by Step (Formula & Amortization Guide)

Understand the mathematical formula behind home, car, and personal loan EMIs, see how monthly interest is amortized, and calculate the savings from prepayments.

By EverySolve Editorial Team • Published: • Last updated: • 6 min read

An Equated Monthly Installment (EMI) is the fixed payment a borrower makes to a lender each month to pay off both the loan principal and the accrued interest over a chosen tenure. While the total monthly payment stays constant on a fixed-rate loan, the internal split between interest and principal changes every single month.

Understanding the reducing-balance EMI formula lets you verify bank loan quotes independently and see why extending a loan tenure by just a few years can double your total interest cost.

The Reducing-Balance EMI Formula

Banks and housing finance companies calculate monthly EMI using the standard reducing-balance formula:

E = P × r × ((1 + r)^n) ÷ ((1 + r)^n - 1)

Where:

  • E = Equated Monthly Installment (monthly payment)
  • P = Principal loan amount borrowed
  • r = Monthly interest rate, calculated as Annual Rate ÷ 12 ÷ 100
  • n = Total number of monthly installments (Years × 12)
Important: Always convert the annual nominal interest rate into a monthly decimal rate before plugging it into the formula. For example, an 8.5% annual rate equals 8.5 ÷ 1200 = 0.00708333 per month.

Worked Example: ₹50,000 Loan at 8.5% for 5 Years

Suppose you take a personal or equipment loan of ₹50,000 at 8.5% p.a. for 5 years (60 months):

  1. Principal (P): ₹50,000
  2. Monthly Rate (r): 8.5 ÷ (12 × 100) = 0.00708333
  3. Tenure in Months (n): 5 × 12 = 60
  4. Growth Factor (1 + r)^n: (1.00708333)^{60} ≈ 1.527301
  5. Monthly EMI (E):
E = 50000 × 0.00708333 × (1.527301) ÷ (1.527301 - 1) = ₹1,025.83

Over the full 60 months:

  • Total Amount Payable: ₹1,025.83 × 60 = ₹61,549.60
  • Total Interest Paid: ₹61,549.60 - ₹50,000 = ₹11,549.60

How Tenure Affects Total Interest (₹10,00,000 Loan at 9.0% p.a.)

Choosing a longer tenure lowers your monthly EMI, but dramatically increases the cumulative interest paid to the lender:

Loan TenureTotal Months (n)Monthly EMITotal Interest PaidTotal Repayment
5 Years60 months₹20,758₹2,45,501₹12,45,501
10 Years120 months₹12,668₹5,20,109₹15,20,109
15 Years180 months₹10,143₹8,25,680₹18,25,680
20 Years240 months₹8,997₹11,59,342₹21,59,342

Notice that stretching a ₹10 Lakh loan from 10 years to 20 years cuts the monthly EMI by only ₹3,671, yet adds ₹6,39,233 in extra interest.

How to Run Your Own Loan Scenarios

  1. Open the EverySolve EMI Calculator (or test early-repayment savings in the Loan Payoff Calculator and borrowing limits in the Loan Eligibility Calculator).
  2. Enter your loan principal, annual interest rate, and tenure in years or months.
  3. Inspect the monthly EMI, total interest outlay, and principal-to-interest ratio immediately to find the shortest tenure that fits comfortably within your monthly budget.
About the EverySolve Editorial Team & Technical Verification:

Mathematical formulas and amortization figures verified using standard reducing-balance monthly compounding equations. EverySolve guides are written and maintained by our engineering and editorial team to document exact formulas, file-format standards, and browser-based workflows.

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Frequently Asked Questions

Why do my early EMI payments go mostly toward interest?

In a reducing-balance loan, each month's interest is calculated on the remaining unpaid principal (Remaining Principal × Monthly Interest Rate r). At the start of a 20-year home loan, the unpaid principal is at its maximum, so interest consumes most of the EMI. As principal is gradually paid down, the interest portion shrinks each month.

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

A flat rate calculates interest on the original full principal for the entire loan tenure, even after you have paid back most of the loan. A 10% flat-rate loan over 5 years actually costs nearly as much as a 17%–18% reducing-balance loan. Always compare loans using reducing-balance APR.

When is the best time to make a part-prepayment on a loan?

Part-prepayments save the most money when made during the first third of the loan tenure, and when you ask the lender to reduce the remaining loan tenure rather than reducing the monthly EMI.

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