Question

A new factory In a small town has an annual payroll of 6 million. It is expected 50% of this money will be spent in the town by factory personnel. The people in the town who receive this money are expected to spend 50% of what they receive in the town , and so on. What is the total of all of this spending , called the total economic impact on the town each year?

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Hermann

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118 Answers

1. Identify the initial spending and the common ratio:

- Initial Spending: 6,000,000

- Common Ratio, r = 0.5

2. Substitute into the formula for the sum of an infinite geometric series:

S = \frac{\text{Initial Spending}}{1 - r}

3. Calculate:

S = \frac{6,000,000}{1 - 0.5}

4. This results in:

S = \frac{6,000,000}{0.5}

5. Simplify the division:

S = 12,000,000

6. Therefore, the total economic impact is 12,000,000 .

- Initial Spending:

- Common Ratio,

2. Substitute into the formula for the sum of an infinite geometric series:

3. Calculate:

4. This results in:

5. Simplify the division:

6. Therefore, the total economic impact is

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