Q.A Fixed Deposit of ₹10,000, compounded yearly for 2 years, matures to ₹14,400. Find the rate of interest per annum.

Form the ratio $A/P$ and recognise it as a perfect square matching $(1+r/100)^2$.

$A/P = 14{,}400/10{,}000 = 1.44 = (1.2)^2$, so $1+r/100=1.2 \Rightarrow r=20$.

Here $P = ₹10{,}000$, $A = ₹14{,}400$, $t = 2$ years, compounded yearly, and the rate $r$ is unknown.

Step 1 — Form the ratio $A/P$.

Step 2 — Match this to $\left(1+\dfrac{r}{100}\right)^2$. Since $(1.2)^2=1.44$,

Check: $10{,}000\times(1.2)^2 = 10{,}000\times1.44 = ₹14{,}400$, matching the given maturity value.

A common error is treating the total growth $A/P = 1.44$ as if it corresponded directly to a $44\%$ rate applied once, forgetting that this growth happened over 2 compounding years — the per-year rate is found by taking the square root of the total growth factor, not by dividing $44\%$ by 2 either (that would be a simple-interest-style shortcut, which does not apply under compounding).