Dynamical Systems

Hey all,
This is like pre differential equations aka dynamical systems.

Here is the problem:
You plan to invest part of your paycheck to finance your childrens education. you want to have enough in the account to draww $1000 a month every month for eight years beginning twenty years from now. The account pays .5% interest each month. a. how much money will you need 20 years from now to accomplish the financial objective? Assume you stop investing whenyour child begins college. b. how much must you deposit per month during the next 20 years? part a answer I have: An+1=1.05An-1000 where A*=b/1-r=-1000/1-1.05=20,000 A* is equillibrium So A96=0 From a thereom in the book I get A96=0=((1.05)^96)c + 20,000 Therefore c=-184.87 To find initial investment: Ao=((1.05)^0)c + 20,000 =-184.87+20,000 =$19,815.10

now for part b. Since its savings nothing is being subtracted per month
An+1=1.05An so Ak=((1.05)^k)A0
so for 240 months we must invest
19815.10=((1.05)^240)c
c=.16
why do i feel as if 16 cents is illogical? any suggestions?