Finding an Unknown Quantity in the EMI Formula

The EMI formula relates four quantities: $P$, $r$, $n$ and $\text{EMI}$. Given any three, the fourth can, in principle, be found by rearranging the formula — but the three quantities are not all equally easy to isolate algebraically.

Finding the principal $P$, given the EMI, the rate and the tenure, is a direct rearrangement:

this simply reverses the three steps of computing an EMI, and is used, for instance, to check how large a loan a borrower can afford given a maximum EMI they can pay. …