Q.A loan of ₹1,00,000 is taken at 12% per annum and repaid through an EMI of ₹8,884.88 per month. Find the tenure of the loan, in months.

Since the tenure cannot be isolated directly (it sits in an exponent), test a few round-number tenures, computing the EMI for each, until the computed EMI matches the given figure — a longer tenure always gives a smaller EMI for the same loan.

Here $P=₹1{,}00{,}000$, monthly rate $r=0.01$, and the given EMI is ₹8,884.88; the tenure $n$ is unknown. Since $n$ appears inside the exponent $(1+r)^n$, it cannot be isolated by a simple rearrangement at this syllabus's scope (no logarithms) — instead, test round-number tenures directly using the EMI formula, relying on the fact that a longer tenure always produces a smaller EMI for the same loan.

Trial 1 — $n=6$ months. $(1.01)^6 = 1.061520$.

$\text{EMI} = \frac{1{,}00{,}000\times0.01\times1.061520}{0.061520} \approx ₹17{,}254.84$ …

Assuming the relationship between tenure and EMI is a simple straight-line one (e.g. "doubling the tenure halves the EMI") is incorrect — the EMI decreases with a longer tenure, but not proportionally, because of the compounding effect inside $(1+r) …