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Financial mathematics-recurrence relations

  1. Nov 8, 2012 #1
    A person has inherited a surplus grain mountain of 30000 tonnes held in a warehouse.each year 5% of the grain is eaten by mice.The person is obliged to add N tonnes each year.find the maximum of N such that mountain will decrease in size.


    This is what I have understood the problem.

    Initial amount=30000 Tonnes
    Each year 5% loss implies remaining amount is 95%.
    N tonnes is added each yer.

    So I can form the recurrence relation as x_n=0.95 x_n-1+N

    But how an I find the maximum of N?


    3. The attempt at a solution
     
  2. jcsd
  3. Nov 8, 2012 #2

    Ray Vickson

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    First: please write the recurrence correctly. What you have written means
    [tex] x_n = 0.95 x_n - 1 + N,[/tex] but maybe you really mean
    [tex] x_n = 0.95 x_{n-1} + N.[/tex] If that is the case, use parentheses:
    x_n = 0.95 x_(n-1) + N.

    Anyway, What is x_0 (assuming time 0 is the beginning of the first year). What is x_1? (Just write it down in detail). Then, what is x_2? Continue for one or two more steps until you see the pattern.

    RGV
     
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