⚡ AZUCATION SHORTCUT:
SI for 3.5 yrs = $18960 - 13920 = 5040$.
SI per year = $5040 / 3.5 = 1440$.
Principal = $13920 - (3 \times 1440) = 9600$.
Rate = $(1440/9600) \times 100 = 15\%$.
CI (Half-yearly, 2 yrs) @ 15%: $r=7.5\%$, $n=4$.
Effective Rate $\approx 33.5\%$. $33.5\% \text{ of } 9600 \approx \mathbf{3221}$.

Step 1: Find the Simple Interest and Principal
Amount after 3 years ($A_1$) = 13920
Amount after 6.5 years ($A_2$) = 18960
Interest for 3.5 years ($6.5 - 3$) = $18960 - 13920 = 5040$.
Interest for 1 year = $5040 / 3.5 = 1440$.
Principal ($P$) = $A_1 - (\text{Interest for 3 years}) = 13920 - (3 \times 1440) = 9600$.

Step 2: Calculate the Rate of Interest
$R = \frac{SI \times 100}{P \times T} = \frac{1440 \times 100}{9600 \times 1} = 15\%$ per annum.

Step 3: Calculate Compound Interest (Compounded Half-Yearly)
For 2 years compounded every 6 months:
$n = 2 \times 2 = 4$ periods.
Rate per period ($r$) = $15\% / 2 = 7.5\%$.
Amount $A = 9600 \times (1 + \frac{7.5}{100})^4 = 9600 \times (1.075)^4$.
$A \approx 9600 \times 1.335469 \approx 12820.5$.
Interest = $12820.5 - 9600 = 3220.5 \approx \mathbf{3221}$.

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