Suppose that the total salary of all the employees at a factory in a certain city is $350,000. Of this salary, 80% is spent in the city. Of the money spent in the city, 80% 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) $2,800,000
B) $504,000
C) $1,400,000
D) $683,200

Question

Quizplus · Accepted Answer

Out of the total salary of $350,000, 80% is spent in the city, which is $280,000. 
Out of this $280,000, 80% is again spent in the city, which is $224,000. 
Continuing this indefinitely, we can write the total amount spent in the city as:

$280,000 + $224,000 + $179,200 + $143,360 + ...

This is a geometric series with first term $280,000$ and common ratio $0.8$. So, using the formula for the sum of an infinite geometric series:

sum = a / (1 - r)

where a is the first term and r is the common ratio, we get:

sum = ($280,000$) / (1 - 0.8) = $1,400,000$

So, a total of $1,400,000 is spent in the city. Therefore, the answer is C.

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