Mr.Smith who deposits 100,000 in a bank on January 1 and then makes withdrawals monthly thereafter beginning February 1. The bank credits interest montly. All answers are numerical.

Hint: In each case think of the bank as paying Mr.Smith an annunity with a PV value of 100,000.

1: Smith withdrawals 1000 on February 1 and then the withdrawals increase by 1% on March 1 and keep increasing by 1% each month thereafter. (Feb is 1000, March 1 is 1010, Apr 1 is 1020.10 and so on.)

Find a) the number of regular withdrawals and

b) the month and

c) the amount of the final smaller withdrawal, if the account earns interest at the rate i^(12) = 9%.