Suppose that the total salary of all the employees at a factory in a certain city is $300,000. Of this salary, 60% is spent in the city. Of the money spent in the city, 60% is again spent in the city. If this continues indefinitely, how much total money is spent in the city, that is, how much of an effect does the original total salary have on the local economy?
A) $1,800,000
B) $288,000
C) $450,000
D) $352,800

Question

Quizplus · Accepted Answer

This is a geometric series with the first term $a = 300,000 \times 0.60 = 180,000$ and common ratio $r = 0.60$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$. Substituting the given values, we get $S = \frac{180,000}{1 - 0.60} = \frac{180,000}{0.40} = 450,000$.

Suppose That the Total Salary of All the Employees at a Factory