The following practical situation illustrates that different ways of aver- aging the same quantity can lead...

 

   

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The following practical situation illustrates that different ways of aver- aging the same quantity can lead to significantly different results. Suppose that one desires to invest money by buying at the beginning of every month a certain number of shares of stock in a company. The cost c, per share depends, of course, on the particular month r and varies from month to month in a fairly unpredictable fashion. Two alternative methods of regular investment suggest themselves: In method A, one buys the same numbers of shares of stock every month; in method B, one buys stock for the same amount of money m every month. After N months, one will then have acquired a total number S of shares of stock and will have paid for them a total amount of money M. The best in- vestment method is clearly that which yields the largest number of shares for the lowest amount of money, i.e., which yields the largest ratio S/M. (a) Obtain an expression for the ratio S/M in the case of method A. (b) Obtain an expression for the ratio S/M in the case of method B. (c) Show that method B is the better investment method, no matter how the cost of shares fluctuates from month to month. [Suggestion: Exploit the ine- quality (iii) of the preceding problem.] inequality is (1) ≥ 1/10) The following practical situation illustrates that different ways of aver- aging the same quantity can lead to significantly different results. Suppose that one desires to invest money by buying at the beginning of every month a certain number of shares of stock in a company. The cost c, per share depends, of course, on the particular month r and varies from month to month in a fairly unpredictable fashion. Two alternative methods of regular investment suggest themselves: In method A, one buys the same numbers of shares of stock every month; in method B, one buys stock for the same amount of money m every month. After N months, one will then have acquired a total number S of shares of stock and will have paid for them a total amount of money M. The best in- vestment method is clearly that which yields the largest number of shares for the lowest amount of money, i.e., which yields the largest ratio S/M. (a) Obtain an expression for the ratio S/M in the case of method A. (b) Obtain an expression for the ratio S/M in the case of method B. (c) Show that method B is the better investment method, no matter how the cost of shares fluctuates from month to month. [Suggestion: Exploit the ine- quality (iii) of the preceding problem.] inequality is (1) ≥ 1/10)

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To obtain expressions for the ratio SM in both method A and method B lets consider the two scenarios separately a Method A In method A the same number s of shares is bought every month for N months Le... View the full answer