Problem Solving

Hi, this question just came in my head...So dunno whether it is valid but your views are invited....

Suppose I take X money (e.g $ 1000) from someone. Now every money I repay back m% (e.g 4%) of the amount which is left with me. e.g. I pay back 4% of $1000 at the end of 1st month...then I will be left with $960...Then at the end of second month I pay back 4% of $960 i.e. $38.4....then I will be left with $960-$38.4 and so forth...

Can someone give me a formula to calculate that after how many months I will be left with y% (e.g. 1%) of the original amount X i.e. $1000


Please see that I cant ever repay back the whole amount since $0 can not be 4% of any amount. I will always be left with some money which I have to repay....

Please reply...

here is your formula:
if N is the principal amount
x is percentage of the remaining amount that you pay, monthly
m is the number of months
y is the percentage of the principal remaining after m months

then this should be the formula to calculate m

(N-(x*N/100))(1-(x/100))^(m-1)=yN/100