Geomatric series

(a) In a Fractional Reserve system of banking, each bank needs only keep a fraction a, say 5%, of its deposits and can lend out 1-a. The loan recipient will then deposit 1 - a at its own bank (could be the same) and use the proceeds as/when needed. The second bank in turn can lend out 1 - a of this amount (1 - a)?, and so on. Compute the Velocity of Money: The total amount of currency generated by each new unit of currency: 1 + (1 - a) + (1 - a)2 + ... What is the velocity of money when a = = 5%? (b) A simple model for a company's stock value is the Dividend Discount Model. It is assumed that the company pays periodic dividends with growth rate g, that is each new periodic dividend Dn+1 = (1+g)Dn. Discounting each future dividend using the same periodic discount rater, the stock value S is computed as the discounted value of future dividends: S=DOC 1+r where Do is the current dividend amount. Using above model, com- pute S as a function of Do,r,g, and provide conditions to ensure the sum converges. Dok7+9