How to Calculate EMI Manually (Formula, Steps & Worked Examples)

Understanding the EMI formula gives you power — you can verify what the bank tells you, compare offers intelligently, and understand exactly why your monthly payment is what it is. Here's the formula, broken down step by step.

Use the CalcHub EMI Calculator for instant results, or follow the manual steps below.

The EMI Formula

EMI = P × r × (1+r)ⁿ / ((1+r)ⁿ − 1)

Where:

• P = Principal loan amount


• r = Monthly interest rate = Annual rate / 12 / 100


• n = Total number of monthly payments (tenure in months)

Step-by-Step Example

Home loan: ₹30,00,000 at 8.5% for 20 years

Step 1: Convert Annual Rate to Monthly

r = 8.5 / 12 / 100 = 0.007083 (monthly rate)

Step 2: Calculate Total Months

n = 20 × 12 = 240 months

Step 3: Calculate (1+r)ⁿ

(1 + 0.007083)²⁴⁰ = (1.007083)²⁴⁰

This is the hard part by hand. Using a calculator:
(1.007083)²⁴⁰ = 5.4365

Step 4: Plug Into Formula

EMI = 30,00,000 × 0.007083 × 5.4365 / (5.4365 − 1) EMI = 30,00,000 × 0.03851 / 4.4365 EMI = 1,15,527 / 4.4365 EMI = ₹26,035 per month

Step 5: Verify

Total paid = 26,035 × 240 = ₹62,48,400 Total interest = 62,48,400 − 30,00,000 = ₹32,48,400

More Worked Examples

Personal Loan: ₹5,00,000 at 14% for 3 years

Step	Calculation	Value
Monthly rate (r)	14/12/100	0.01167
Total months (n)	3 × 12	36
(1+r)ⁿ	(1.01167)³⁶	1.5178
Numerator	5,00,000 × 0.01167 × 1.5178	8,856
Denominator	1.5178 − 1	0.5178
EMI	8,856 / 0.5178	₹17,103
Total interest	(17,103 × 36) − 5,00,000	₹1,15,708

Car Loan: ₹8,00,000 at 9% for 5 years

Step	Calculation	Value
Monthly rate (r)	9/12/100	0.0075
Total months (n)	5 × 12	60
(1+r)ⁿ	(1.0075)⁶⁰	1.5657
EMI	₹16,607
Total interest	(16,607 × 60) − 8,00,000	₹1,96,420

Understanding Each Component

Why the Monthly Rate Matters

The difference between 8% and 9% annual seems small, but over 20 years on ₹30 lakh:

Annual Rate	Monthly Rate	EMI	Total Interest	Difference
8.0%	0.00667	₹25,093	₹30,22,280	—
8.5%	0.00708	₹26,035	₹32,48,400	+₹2,26,120
9.0%	0.00750	₹26,992	₹34,78,080	+₹4,55,800
9.5%	0.00792	₹27,963	₹37,11,120	+₹6,88,840

A 1.5% rate difference costs ₹6.89 lakh in extra interest.

Why Tenure Matters

₹30 lakh at 8.5%:

Tenure	EMI	Total Interest	Interest as % of Loan
10 years	₹37,224	₹14,66,880	49%
15 years	₹29,543	₹23,17,740	77%
20 years	₹26,035	₹32,48,400	108%
25 years	₹24,106	₹42,31,800	141%
30 years	₹23,060	₹53,01,600	177%

At 30 years, you pay ₹53 lakh in interest — 1.77× the loan amount.

The Amortization Breakdown

In early months, most of your EMI pays interest, not principal:

₹30L at 8.5%, 20 years, EMI ₹26,035:

Month	EMI	Interest	Principal	Balance
1	₹26,035	₹21,250	₹4,785	₹29,95,215
12	₹26,035	₹20,883	₹5,152	₹29,40,847
60	₹26,035	₹18,686	₹7,349	₹26,27,960
120	₹26,035	₹14,709	₹11,326	₹20,46,820
180	₹26,035	₹8,235	₹17,800	₹11,18,150
240	₹26,035	₹183	₹25,852	₹0

In month 1, only ₹4,785 (18%) goes to principal. By month 180, ₹17,800 (68%) goes to principal. This is why prepayments early in the loan save the most money.

Simplified Approximation (Without Calculator)

For quick mental estimates: EMI ≈ P × r × 1.1ⁿ/¹² / (1.1ⁿ/¹² − 1) is too complex mentally. Instead use: Quick estimate: EMI ≈ P / n + P × r / 2

This overestimates slightly but gives a ballpark:
₹30L, 240 months, r = 0.00708:
EMI ≈ 30,00,000/240 + 30,00,000 × 0.00708/2
≈ 12,500 + 10,620 = ₹23,120 (actual: ₹26,035 — off by 11%, but useful for quick mental math)

How to Use the Calculator

For exact results without manual calculation:

1. Open the CalcHub EMI Calculator


2. Enter loan amount, interest rate, tenure


3. See: exact EMI, total interest, amortization schedule

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Can I calculate EMI in Excel?

Yes. Use the PMT function: =PMT(rate/12, months, -principal)

For ₹30L at 8.5% for 20 years: =PMT(8.5%/12, 240, -3000000) = ₹26,035

What changes EMI more — rate or tenure?

On a ₹30L loan, reducing rate from 9% to 8% saves ₹1,899/month. Reducing tenure from 20 to 15 years increases EMI by ₹3,508/month but saves ₹9.31 lakh in total interest. Rate reductions save monthly; tenure reductions save total cost.

Is EMI calculated on reducing balance or flat rate?

Banks use reducing balance (the standard EMI formula above). Some NBFCs and dealer finance use flat rate (simple interest on original principal), which looks cheaper but is actually 1.8–2× more expensive. Always ask which method is used.

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Related Calculators

• Loan EMI Calculator — instant EMI calculation
• Home Loan Calculator — housing loan specific
• Personal Loan EMI Calculator — personal loan EMI
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