Q.A borrower pays an EMI of ₹21,116.42 per month for 10 months on a loan taken at 12% per annum. Find the loan amount.

This is the EMI formula used in reverse — rearrange for $P$ using the given EMI, monthly rate and tenure.

$(1.01)^{10}=1.104622$. …

Here $\text{EMI}=₹21{,}116.42$, annual rate $12\%$ so monthly rate $r=0.01$, tenure $n=10$ months, and the loan amount $P$ is unknown.

Step 1 — Compute $(1+r)^n$.

Step 2 — Rearrange the EMI formula for $P$.

Step 3 — Evaluate. …

A frequent inversion error is multiplying the EMI by $\dfrac{r(1+r)^n}{(1+r)^n-1}$ instead of by its reciprocal $\dfrac{(1+r)^n-1}{r(1+r)^n}$ — since a loan's principal must always be larger than a single EMI (for any tenure of more than one …