[SOLVED] Suppose that the Federal Reserve creates $100

Suppose that the Federal Reserve creates $100 million of new money, as in Exercise 41, and the banks lend 85% of all new money they receive. However, suppose that out of each loan, only 80% is redeposited into the banking system. Thus, whereas the first set of loans totals (.85)(100) million dollars, the second set is only 85% of (.80)(.85)(100), or (.80)(.85)2(100) million, and the next set is 85% of (.80)2(.85)2(100), or (.80)2(.85)3(100) million dollars, and so on. Compute the total theoretical amount that may be loaned in this situation.

Exercise 41:
Suppose that the Federal Reserve (the Fed) buys $100 million of government debt obligations from private owners. This creates $100 million of new money and sets off a chain reaction because of the “fractional reserve” banking system. When the $100 million is deposited into private bank accounts, the banks keep only 15% in reserve and may loan out the remaining 85%, creating more new money: (.85)(100) million dollars. The companies that borrow this money turn around and spend it, and the recipients deposit the money in their bank accounts. Assuming that all the (.85)(100) million is redeposited, the banks may again loan out 85% of this amount, creating (.85)2 (100) million additional dollars. This process may be repeated indefinitely. Compute the total amount of new money that can be created theoretically by this process, beyond the original $100 million. (In practice, only about an additional $300 million is created, usually within a few weeks of the action of the Fed.)

Question: Suppose that the Federal Reserve creates $100