Identify Given Values

Note down the principal, rate, and time given in the problem: Principal $P = 4000$, Rate $R = 12\%$, and Time $T = 9$ months.

$P = 4000, R = 12\%, T = 9 \text{ months}$

Convert Time to Years

Since the rate is per annum, convert the time from months to years by dividing by 12: $T = \frac{9}{12} = \frac{3}{4}$ years.

$T = \frac{9}{12} = 0.75 \text{ years}$

Apply Simple Interest Formula

Substitute the values into the simple interest formula: $SI = \frac{P \times R \times T}{100}$.

$SI = \frac{4000 \times 12 \times \frac{3}{4}}{100}$

Calculate the Final Value

Perform the multiplication and division: $SI = \frac{4000 \times 9}{100} = 40 \times 9 = 360$.

$SI = 360$