1074 - Dis-interest

Time Limit: 2s Memory Limit: 128MB

Submissions: 340 Solved: 24
Description
Dominic has his own business. He sells widgets. He doesn't really like selling widgets, he just sells them so that one day he can buy a Nintendo Wii. Everyone knows that a Wii costs G dollars. That is Dominic's one and only goal, if he achieves that then he is a success. Dominic decided that he must get his Wii after M months of working. Further he knows he can sell exactly one widget per month, but he can decide the price that he sells the widgets for. He must sell them at a high enough price that he meets his goal, but he also wants to sell them at the lowest price possible, so that his customers don't get too mad. Dominic also knows he can invest the money he has already made at an interest rate of R. Every month he is payed R percent of what he has at the begining of the month. If mathematically a fraction of a cent is to be paid in interest, then that fraction is ignored. It is your job to determine for what price Dominic is to sell each widget. For example, let's say that Dominic sells his widgets for $100 and that the interest rate is .1 or 10%. In the first month he sells one widget and ends up with $100. In the second month he sells another widget for $100 and makes $10 on interest, so he winds up with $210. During the third month he makes another $100 from selling a widget and earns $21 in interest, making his total $331. Finally during the fourth month he sells yet another widget for $100 and gets $33.10 in interest giving him $464.10.
Input
There will be several test cases. Each test case will consist of a line with three numbers, M, R, and G. M and R will be positive integers less than 100. G will be a positive floating point number with exactly two digits after the decimal. G will be at most 1000.
Output
For each test case, output a line that says "Dominic needs to set the price at P." where P is the price that Dominic needs to set. P should be a floating point number with exactly two digits after the decimal. If P is less than 1 then the output should have a leading 0 before the decimal point.
Sample Input
2 10 210.00
3 10 331.00
4 10 464.10
10 7 250.00
Sample Output
Dominic needs to set the price at $100.00.
Dominic needs to set the price at $100.00.
Dominic needs to set the price at $100.00.
Dominic needs to set the price at $18.10.
Hint
Source