1. The problem is to calculate the value of $A$ given by the formula $A = 2500\left(1 + \frac{1}{12}\right)$. 2. This formula represents a simple arithmetic expression where you add $1$ and $\frac{1}{12}$, then multiply the result by $2500$. 3. First, calculate the sum inside the parentheses: $$1 + \frac{1}{12} = \frac{12}{12} + \frac{1}{12} = \frac{13}{12}$$ 4. Now multiply $2500$ by $\frac{13}{12}$: $$A = 2500 \times \frac{13}{12} = \frac{2500 \times 13}{12} = \frac{32500}{12}$$ 5. Simplify the fraction by performing the division: $$A = 2708.33\overline{3}$$ 6. Therefore, the value of $A$ is approximately $2708.33$. Note: The user provided two values $2970.68$ and $4016.27$ which do not correspond to this calculation. Final answer: $$A \approx 2708.33$$