Formula to calculate EMI

This is the formula to caluculate:

E = P×r×(1 + r)ⁿ/((1 + r)ⁿ - 1)

E is EMI

where P is Priniple Loan Amount

r is rate of interest calualted in monthly basis it should be = Rate of Annual interest/12/100

if its 10% annual ,then its 10/12/100=0.00833

n is tenture in number of months

Eg: For 100000 at 10% annual interest for a period of 12 months

it comes  to 100000*0.00833*(1 + 0.00833)¹²/((1 + 0.00833)¹² - 1) = 8792

credit goes to rmathew

Good one. thanks mate for posting it.

great mate could u pls also provide the derivation of the formula i.e how u get this formula from basic compound interest formula.

amar

Prasanth

That was helpful. And could you request Mathew to provide as Amar has requested above.

Selva Kumar

Suppose you take on a loan for P Rupees, the tenure of the loan is n months (for example, n=240 for a 20-year loan), the monthly rate of interest is r (usually calculated by dividing the annual rate of interest quoted by the bank by 12, the number of months in a year, and dividing that by 100 as the rate is usually quoted as a percentage) and E Rupees is the EMI you have to pay every month. Let us use P_i to denote the amount you still owe to the bank at the end of the i-th month. At the very beginning of the tenure, i=0 and P₀=P, the principal amount you took on as a loan.

At the end of the first month, you owe the bank the original amount P, the interest accrued at the end of the month r×P and you pay back E. In other words:

or to rewrite it slightly differently:

Similarly, at the end of the second month the amount you still owe to the bank is:

or substituting the value of P₁ we calculated earlier:

and once again expanding it and rewriting it slightly differently:

where "x^y" denotes "x raised to the power y" or "x multiplied by itself y times". To make this look slightly simpler, we substitute "(1 + r)" by "t" and now it looks like this:

Continuing in this fashion and calculating P₃, P₄, etc. we quickly see that P_i is given by:

At the end of n months (that is, at the end of the tenure of the loan), the total amount you owe to the bank should have become zero. In other words, P_n=0. This implies that:

which means that:

We can simplify this further by noticing that we have a  of n terms here with a common ratio of t and a scale factor of 1. The sum of such a series is given by "(tⁿ - 1)/(t - 1)", which we substitute in the above equation to yield:

which can be rewritten as:

which can again be rewritten by substituting the value of t back as "(1 + r)" as:

and this is the formula for calculating your EMI.

Sourced from here

http://www.contractorindia.com/Planning_Tools/loan-amortization-schedule.xls

That was COOL!

Thanks

Selva Kumar

Too many derivations  but its a nice job...

Use this link for easy calculation;   

http://www.rupeetimes.com/calculators/personal_loan/personal_loan_emi_calculator.php?download=0&btnClicked=btnSubmit&loan=1&duration=1&rate=1&advance_emi=1

So what do you think, I am Smart hah.. 

hey ...that was good

There is an easier way - Use the PMT function in Excel - Hit F1 in Excel to know how to use it, or google. Much easier, and quick results, without any math!