The EMI Formula

For a loan of principal $P$, at a monthly interest rate $r$ (as a decimal), repaid over $n$ equal monthly instalments, the EMI is

Why the formula takes this shape: the EMI is set so that the present value of all $n$ future monthly payments, discounted back to today at the monthly rate $r$, exactly equals the loan amount $P$ — this is the same present-value idea behind the formula, though this chapter does not require deriving it from first principles; the formula itself, applied correctly, is the syllabus's scope.

Getting the monthly rate right is the step where most errors happen: banks always quote loan interest as an annual rate, so it must first be converted to a monthly rate before it can go into the formula.