Find the compound interest on ₹12,000 at 8% per annum for 2 years 9 months, interest compounded annually.

The correct option is ₹2,837.

Step 1: Understand the given values
Principal ($P$) = ₹12,000
Rate of interest ($R$) = 8% per annum
Time ($T$) = 2 years 9 months

Step 2: Convert the time into years
9 months can be written in years as:
$\frac{9}{12}=\frac{3}{4}$ years.
So, the total time period is $2\frac{3}{4}$ years.

Step 3: Calculate the Amount for compound interest compounded annually
When time is given in a fractional form like $n\frac{a}{b}$ years, the compound interest amount formula is:
$A=P\times {\left(1+\frac{R}{100}\right)}^n\times \left(1+\frac{\frac{a}{b}\times R}{100}\right)$

Here, $n=2$ and $\frac{a}{b}=\frac{3}{4}$.
Substitute the values into the formula:

$A=12000\times {\left(1+\frac{8}{100}\right)}^2\times \left(1+\frac{\frac{3}{4}\times 8}{100}\right)$

Simplify the terms inside the brackets:

$1+\frac{8}{100}=1+\frac{2}{25}=\frac{27}{25}$

$1+\frac{6}{100}=1+\frac{3}{50}=\frac{53}{50}$

Now calculate the total amount:

$A=12000\times {\left(\frac{27}{25}\right)}^2\times \frac{53}{50}$

$A=12000\times \frac{729}{625}\times \frac{53}{50}$

$A=240\times \frac{729}{625}\times 53$

$A=\frac{9273120}{625}=14836.992\approx 14,837$

Step 4: Calculate the Compound Interest (C.I.)
$\text{Compound Interest}=A-P$

$\text{C.I.}=14837-12000=2837$

Thus, the compound interest is approximately ₹2,837.