Let's simplify the given expression step by step. The expression is:

$T = 5000 + 108,000 \times \left[0.002 \times 936 \times \frac{32.4 - 12}{12}\right]$

First, simplify inside the brackets:

1. Calculate the difference inside the fraction: $32.4 - 12 = 20.4$

2. Divide the result by 12: $\frac{20.4}{12} = 1.7$

Now, the expression becomes: $T = 5000 + 108,000 \times \left[0.002 \times 936 \times 1.7\right]$

3. Multiply the constants inside the brackets: $0.002 \times 936 = 1.872$

$1.872 \times 1.7 = 3.1824$

4. Multiply by 108,000: $108,000 \times 3.1824 = 343,699.2$

5. Add 5000 to the result: $T = 5000 + 343,699.2 = 348,699.2$

Thus, the simplified value of $T$ is:

$T = 348,699.2$

Would you like more details or have any questions? Here are some questions you might find interesting:

1. What is the distributive property in algebra?
2. How do you simplify complex fractions?
3. Can you explain how to solve systems of linear equations?
4. What are the properties of exponents?
5. How do you find the area under a curve using integration?

Tip: When simplifying expressions, always follow the order of operations: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).