Federal Reserve BankingSuppose that the FederalReserve

Chapter 11, Problem 42

(choose chapter or problem)

Federal Reserve BankingSuppose that the FederalReserve creates $100 million of new money, as in Ex-ercise 41, and the banks lend 85% of all new money theyreceive. However, suppose that out of each loan, only 80%is redeposited into the banking system. Thus, whereas thefirst set of loans totals (.85)(100) million dollars, the sec-ond 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. Computethe total theoretical amount that may be loaned in thissituation.PerpetuitySuppose that, when you die, the proceeds of a lifeinsurance policy will be deposited into a trust fund that will earn 8%interest, compounded continuously. According to the terms of yourwill, the trust fund must pay to your descendants and their heirsc1dollars (total) at the end of the first year,c2dollars at the end of thesecond year,c3dollars at the end of the third year, and so on,forever. The amount that must be in the trust fund initially to make thekth payment iscke.08k, the present value of the amount to be paidinkyears. So the life insurance policy should pay a total of?k=1cke.08kdollars into the trust fund to provide for all thepayments.