The compound interest on Rs. 12,000 for 9 months at $20\%$ per annum, interest being compounded quarterly is:

Given:
* Principal ($P$) = Rs. 12,000
* Time ($t$) = 9 months = $\frac{9}{12}=\frac{3}{4}$ year
* Annual Rate ($R$) = $20\%$ per annum

Since interest is compounded quarterly:

* Number of conversion periods ($n$) = $4\times t=4\times \frac{3}{4}=3$ periods
* Quarterly rate ($r$) = $\frac{R}{4}=\frac{20\%}{4}=5\%$ per quarter

The formula for the amount ($A$) is:

$$A=P{\left(1+\frac{r}{100}\right)}^n$$

$$A=12000{\left(1+\frac{5}{100}\right)}^3$$

$$A=12000{\left(\frac{21}{20}\right)}^3$$

$$A=12000\times \frac{9261}{8000}$$

$$A=1.5\times 9261$$

$$A=\text{Rs. }13891.50$$

Compound Interest ($CI$) = $A-P$

$$CI=13891.50-12000=\text{Rs. }1891.50$$