Explanation:

- The sum grows to Rs 13650 at 15% per annum simple interest after 2 years.

- Using the simple interest formula $A=P(1+rt)$, we can determine the principal $P$.

- Here, $A=13650$, $r=0.15$, $t=2$.

- Solve for $P$: $13650=P(1+0.15\times 2)$.

- $P=\frac{13650}{1.3}=10500$.

- For the compound interest calculation:

- Principal $P=10500$, rate $r=15\mathrm{\%}$ annually (7.5% half-yearly).

- For 1 year (2 half-years):

- Final amount $A=P(1+0.075{)}^2$.

- Calculate:

$$A=10500\times (1+0.075{)}^2$$

$$A=10500\times (1.075{)}^2$$

$$A=10500\times 1.155625$$

$$A\approx 12134$$

- ?? Correct answer is 12134.

My assessment: “”