solve {(107 * 0.25^(0) / (1 +0.10)^1 +  (107 * 0.25^(1) / (1 +0.10)^2  + (107 * 0.25^(2) / (1 +0.10)^3  + (107 * 0.25^(3) / (1 +0.10)^4  + (107 * 0.25^(4) / (1 +0.10)^5  + (107 * 0.25^(5) / (1 +0.10)^6)} - 1000

The value of the given expression is approximately \(-874.13\).

Let's break it down step-by-step:

\[ 
\text{CLV} = \left( \frac{107 \cdot 0.25^0}{(1 + 0.10)^1} + \frac{107 \cdot 0.25^1}{(1 + 0.10)^2} + \frac{107 \cdot 0.25^2}{(1 + 0.10)^3} + \frac{107 \cdot 0.25^3}{(1 + 0.10)^4} + \frac{107 \cdot 0.25^4}{(1 + 0.10)^5} + \frac{107 \cdot 0.25^5}{(1 + 0.10)^6} \right) - 1000
\]

Calculating each term:

1. \(\frac{107 \cdot 0.25^0}{(1 + 0.10)^1} = \frac{107}{1.1} = 97.27\)
2. \(\frac{107 \cdot 0.25^1}{(1 + 0.10)^2} = \frac{107 \cdot 0.25}{1.21} = 22.15\)
3. \(\frac{107 \cdot 0.25^2}{(1 + 0.10)^3} = \frac{107 \cdot 0.0625}{1.331} = 5.02\)
4. \(\frac{107 \cdot 0.25^3}{(1 + 0.10)^4} = \frac{107 \cdot 0.015625}{1.4641} = 1.14\)
5. \(\frac{107 \cdot 0.25^4}{(1 + 0.10)^5} = \frac{107 \cdot 0.00390625}{1.61051} = 0.26\)
6. \(\frac{107 \cdot 0.25^5}{(1 + 0.10)^6} = \frac{107 \cdot 0.0009765625}{1.771561} = 0.06\)

Summing these values:
\[ 97.27 + 22.15 + 5.02 + 1.14 + 0.26 + 0.06 = 125.90 \]

Subtracting the acquisition cost:
\[ 125.90 - 1000 = -874.10 \]

Thus, the CLV for the given parameters is approximately \(-874.13\), indicating a negative value which implies that the customer is not profitable under these conditions.

Do you have any questions or need further details?

Here are 5 numbered questions you might consider asking next:
1. How can the negative CLV be interpreted in a business context?
2. What strategies can be employed to turn a negative CLV into a positive one?
3. Can you explain the impact of each parameter (retention rate, discount factor, etc.) on the CLV?
4. How would increasing the retention rate affect the CLV calculation?
5. What are some examples of businesses successfully improving their CLV through customer retention strategies?

**Tip:** When calculating complex formulas, breaking them down into smaller steps and understanding the contribution of each part can help in identifying areas for improvement.

Learn how to calculate Customer Lifetime Value (CLV) step-by-step with a detailed explanation. This problem involves compound interest and discounting, crucial for business analytics and financial modeling. Suitable for advanced high school students and beyond.

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