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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
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.
That was helpful. And could you request Mathew to provide as Amar has requested above.
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:
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 "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:
Continuing in this fashion and calculating P3, P4, etc. we quickly see that Pi 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, Pn=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
That was COOL!
Too many derivations but its a nice job...
Use this link for easy calculation;
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!
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