Its a geometric series. In math: Let r=(1-reserve requirement) and Total = 1000 * sum(1-r^n,n=0,infinity) = 1000 * 1/(1-r)
Now I'm probably wrong with my indices because I'm a little confused about connecting my infinite sum to people running around at the bank. If I plut in .8 for r (the same as the comment above used, I get 1/(1-.8)=5, or $5,000 so I'm right that far. For 10% its: 1/(1-.9) = 10 or $10,000. So the author is right in numbers, but arguing against this would be ridiculous. How could any bank guard against this? Why would they want to?
Now I'm probably wrong with my indices because I'm a little confused about connecting my infinite sum to people running around at the bank. If I plut in .8 for r (the same as the comment above used, I get 1/(1-.8)=5, or $5,000 so I'm right that far. For 10% its: 1/(1-.9) = 10 or $10,000. So the author is right in numbers, but arguing against this would be ridiculous. How could any bank guard against this? Why would they want to?