To solve the expression $500\left[\frac{\left(1+0.00875\right)^{43}-1}{0.00875}\right]$, we will follow these steps:

1. Calculate the base: $1 + 0.00875 = 1.00875$.

2. Raise the base to the power of 43: $(1.00875)^{43}$

3. Subtract 1 from the result: $(1.00875)^{43} - 1$

4. Divide the result by 0.00875: $\frac{(1.00875)^{43} - 1}{0.00875}$

5. Multiply by 500: $500 \times \left[\frac{(1.00875)^{43} - 1}{0.00875}\right]$

Now, let's compute each step.

Step-by-Step Calculation:

1. Base: $1.00875$
2. Power: $(1.00875)^{43} \approx 1.468085$
3. Subtract 1: $1.468085 - 1 = 0.468085$
4. Divide: $\frac{0.468085}{0.00875} \approx 53.495429$
5. Multiply by 500: $500 \times 53.495429 \approx 26747.7145$

So, the final result is approximately 26,747.71.

Would you like any details or have any questions? Here are some related questions:

1. What is the formula for compound interest?
2. How does changing the interest rate affect the final value in a compound interest calculation?
3. What is the impact of increasing the number of periods on the future value in an annuity?
4. How would the result change if the interest rate was compounded continuously?
5. What are the applications of this formula in finance?

Tip: Always ensure that your calculator is set to the correct mode (degrees/radians) for trigonometric calculations, or decimal precision for financial computations!