Suppose a man has $ 100,000 saving in a bank when he retires. Then, he receives

Question

Suppose a man has $ 100,000 saving in a bank when he retires. Then, he receives $20,000 social security benefit each year and pays no tax, but he needs to spend $30,000 each year for living. He put all money in the bank and the bank gives him 5% yearly interest. Let An represent the amount of money he will have after n years. So, we have A0 = 100,000, A1 =(100,000+20,000-30,000)+(100,000+20,000- 30,000)x5% = 90000x1.05 = 94500. (a) Find a recurrence relation for computing An and solve it. (We assume that if the balance becomes negative, the interest will be negative, which means the man gives the bank 5% interests.) (b) How many years the man has enough money to live before the balance becomes red (negative)?

Explanation / Answer

R = 5% =   0.05 A(0)= 100000 S.S.B= 20000 $/YR EXP. 30000 $/YR WITHDRL 10000 $/YR A

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