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Formula to calculate EMI

Pages : 123
#1 22-Apr, 2009 05:47 PM
Prasanth
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Joined Date: 09 Apr 2009
Location: Vijaywada
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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



Last Updated: 22-Apr, 2009 05:50 PM, by prasanth11
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#2 09-May, 2009 08:22 PM
Sachin Dutta
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Good one. thanks mate for posting it.



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#3 08-Aug, 2009 02:56 PM
Amar
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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



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#4 13-Aug, 2009 02:26 PM
Selva Kumar
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Prasanth

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

Selva Kumar




Never mind what others say, do whats right for that moment!
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#5 13-Aug, 2009 03:51 PM
Prasanth
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Joined Date: 09 Apr 2009
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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 Pi 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:

P1 = P + r×P - E


or to rewrite it slightly differently:

P1 = P×(1 + r) - E


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

P2 = P1×(1 + r) - E


or substituting the value of P1 we calculated earlier:

P2 = (P×(1 + r) - E)×(1 + r) - E


and once again expanding it and rewriting it slightly differently:

P2 = P×(1 + r)2 - E×((1 + r) + 1)


where "xy" 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:

P2 = P×t2 - E×(1 + t)


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

Pi = P×ti - E×(1 + t + t2 + ... + ti-1)


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, Pn=0. This implies that:

Pn = P×tn - E×(1 + t + t2 + ... + tn-1) = 0


which means that:

P×tn = E×(1 + t + t2 + ... + tn-1)


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:

P×tn = E×(tn - 1)/(t - 1)


which can be rewritten as:

E = P×tn×(t - 1)/(tn - 1)


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

E = P×r×(1 + r)n/((1 + r)n - 1)


and this is the formula for calculating your EMI.

Sourced from here



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#6 13-Aug, 2009 09:21 PM
greenhorn
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#7 18-Aug, 2009 02:13 PM
Selva Kumar
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That was COOL!

Thanks

Selva Kumar




Never mind what others say, do whats right for that moment!
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#8 18-Aug, 2009 03:05 PM
Alex
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Joined Date: 02 Jun 2009
Location: Bangalore
Posts: 86
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Too many derivations Sealed but its a nice job...Wink

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.. Innocent



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#9 29-Apr, 2010 09:59 PM
Abhisek Das
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Joined Date: 03 Apr 2010
Location: Kolkata
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hey ...that was good



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#10 29-Apr, 2010 10:32 PM
Krishna
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Joined Date: 10 Jan 2009
Location: Noida
Posts: 3525
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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!



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