# How to calculate EMI?

In our daily life we face enormous application of mathematics. Calculation of equated monthly installments (EMI) for car or home loan is one such common application of mathematics.

EMI or equated monthly installments is the most popular form of loan payment. It is a fixed amount of repayment made every month towards the loan, which includes payment towards both principal and interest. Most of us always believe the bank executives blindly on the figure which they quote as EMI.

This post is to explain the mathematics behind EMI and how to calculate it in excel using inbuilt excel function.

**Calculation of EMI**

EMI= P x r x (1 + r)^n / ((1+r)^n -1)** **

Here p = principal amount (loan taken)

r = interest rate per month (ex: if interest rate per annum is 10% then 10/(12*100))

n= tenure in months

** **

**For example**,

EMI = 100000*0.01*(1+0.01)^24 /((1+0.01)^24 -1) = **4707**

Where,

p = loan taken = 1,00,000

r = interest rate per month = 1% = 0.01

n= tenure in months = 2 Years = 24 months

This formula assumes, EMI payment is made at the end of each period (month). This is also called EMI in arrears. If EMI is paid at the beginning of each period it is called EMI in advance.

Further additions will be done on EMI for any other processing fee or possible charges which may be applicable as per the rules of financing institutions (bank).

In excel it is very simple to calculate EMI. There is an inbuilt formula for EMI calculation called **PMT**

**PMT(rate,nper,pv)**

Where,

Rate – Interest rate for the loan.

nper – Total number of payments for the loan.

PV – Present value/principal or loan taken.

FV – Future value (you can omit it)

Type – we have to put the value either 0 or 1. If payments are made at the beginning (EMI in advance) of each period, 1 is used. If EMI payments are made at the end of the period (EMI in arrears) put 0. If omitted 0 is taken a default value.

Lot more can be discussed about EMI. Please share your knowledge, doubts or experiences with EMI calculations by posting comments below.

**Author – Vineet Patawari**

Hello every1.

I have a problem,please help me with a solution of following…

An amount of 9270 is to be returned in 3 equal installments. If rate of intrst is 3%per annum then find each installment value.

Give a shortcut formula also if available please.

The Answer is 3091.287589

How did u calculate this. ? Please explain…

Mr. Manoj Swami

I have Found out a new formula for this to do, not only this we can do lot or all calculations relating to EMI calculator, I think you did not visited my Blog please visit and Download my new type of EMI Calculator

My Blog Link is: http://emicalculator3types.blogspot.in/

Main thing in this blog is my New Type of EMI Calculator download it, if you do not download the EMI calculator wast of visiting my Blog, I have given so many links on the top of my blog all are same, so download from any one of the link and one more thing if you see the Normal Formula for calculating which i have given in the blog it is totally different formula because i have found out the formula again which is already exist instead of taking the existing formula from books or Website

There is no shot cut formula for 3 months. There is shot cut formula for 2 months but i don’t no the formula, i saw the formula in some book.

Is there formula for reverse calculation? Eg: EMI, P, R are known. Need to find the tenure.

Just Download EMI Calculator from this link: http://emicalculator3types.blogspot.in/

and select 3 rd type of EMI Calculator in downloaded software, you will get Answer, if any doubts please contact me.

There are there 3 of EMI Calculators

Download 3 Types of EMI Calculators: http://emicalculator3types.blogspot.com/

Formula for Calculate EMI is:

p x (((i/12) + 100)/100)^t

________________________________________________________________________

1 + (((i/12) + 100)/100) + (((i/12) + 100)/100)^2 + ——— + (((i/12) + 100)/100)^t-1

Where:

P is Principal

I is Rate of Interest per Annam

T is Tenure

I had a bad experience with a bank. Out of the total amount refunded every year, they were bifurcating it into principal refund and interest refund. Per year their interest was about Rs 10000/= more than what it should have been. I persisted with my calculation and after many months they admitted that there was a bug in their software and thanked me for getting hold of it.

Better to be careful with the calculations.

I had suggested a thumb rule which is quite useful in comparing different loan propositions and possible EMI.

The thumb rule is

EMI is slightly more than P * (r/2 + 1/n) where P = principal, r = rate of interest per month, n = number of months.

nice one………..!!!!!!

A rough estimate of EMI can be arrived at without calculator/excel as follows:

EMI = p * (r/2 + 1/n)

In your example: p = 100,000, r = 0.01, n = 24 then EMI = 100000 * (0.005 + 0.04) = 4500.

Your actual calculation yielded 4707.

A rough estimate of EMI can be arrived at without calculator/excel as follows:

EMI = p * (r + 1/n)

In your example: p = 100,000, r = 0.01, n = 24 then EMI = 100000 * (0.01 + 0.04) = 5000.

This estimate is always slightly higher than the actual figure.

Your actual calculation yielded 4707.

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