5. A bank account earns 5% interest compounded monthly. Suppose that $1000 is initially deposited into the account, but that $10 is withdrawn every month. (a) Show that the amount in the account after n-months is (1+) An-1 – 10, Ao = 1000. 0.05 12 An (b) How much money will be in the account after 1 year? (c) Suppose that instead of $10, a fixed amount d dollars is withdrawn each month. Find the value of d such that the amount in the account after each month remains $1000. (d) What happens if d is greater than this amount? (e) This problem deals with money and savings accounts. The concept behind this construction is much more general. Describe a further application, outside the realm of economics, where this model might be applied.

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