Q.Find the amount and compound interest on ₹16,000 for 9 months at 20% per annum, compounded quarterly.

For quarterly compounding, divide the annual rate by 4 and multiply the time in years by 4 to get the number of periods.

9 months $= 0.75$ year, so periods $= 4 \times 0.75 = 3$; rate per quarter $= 20/4 = 5\%$. …

Here $P = ₹16{,}000$, annual rate $r = 20\%$, time $= 9$ months, compounded quarterly.

Step 1 — Convert the time to years, then to quarters. $9$ months $= \dfrac{9}{12} = 0.75$ year. Number of quarterly periods $= 4t = 4 \times 0.75 = 3$. Rate per quarter $= \dfrac{r}{4} = \dfrac{20}{4} = 5\%$.

Step 2 — Apply the quarterly formula.

$A = P\left(1+\frac{r}{400}\right)^{4t} = 16{,}000\left(1+\frac{20}{400}\right)^{3} = 16{,}000(1.05)^{3}$ …

Misreading 9 months as $t=9$ (years) instead of converting it to $0.75$ year is a common error, as is forgetting that the quarterly rate is $r/4$, not $r/2$. Always convert the given time into …