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Financial Expression 401674

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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.