Financial Expression 401674
1. **State the problem:** We need to evaluate the expression $$\frac{3,235,000}{\left[\frac{\left(1 + \frac{0.04}{2}\right)^6 - 1}{\frac{0.04}{2}}\right]}$$ which involves a fraction with a compound interest-like term in the denominator.
2. **Identify the formula and rules:** The denominator resembles the formula for the sum of a geometric series or an annuity factor: $$\frac{(1 + r)^n - 1}{r}$$ where $r = \frac{0.04}{2} = 0.02$ and $n = 6$.
3. **Calculate the denominator step-by-step:**
- Compute $r = 0.02$
- Compute $(1 + r)^n = (1.02)^6$
Calculate $(1.02)^6$:
$$ (1.02)^6 = 1.02 \times 1.02 \times 1.02 \times 1.02 \times 1.02 \times 1.02 = 1.126162419 $$ (approx)
- Subtract 1:
$$ 1.126162419 - 1 = 0.126162419 $$
- Divide by $r$:
$$ \frac{0.126162419}{0.02} = 6.30812095 $$ (approx)
4. **Calculate the entire expression:**
$$ \frac{3,235,000}{6.30812095} \approx 512,726.68 $$
5. **Interpretation:** The value of the given expression is approximately 512,726.68.
This completes the evaluation.