9. A deposit of $100,000 is made to an investment fund at the beginning of a year. On the last day of each year two dividends are awarded. The first dividend is 20% of the amount in the account during that year. The second divi- dend is 45% ofthe amount in the account in the previous year. a) Find a recurrence relation for {Pnl, where Pn is the amount in the account at the end ofn years ifno money is ever withdrawn.

b) has been withdrawn?