Asumming an ideal world situation where amount can be deposited in paise.teh acc to qustion let the initial amount be x.
after the end of first year amount left=2*x-65
after second year amount left=2*(2*x-65)-65=4*x-(2^2-1)*65
after third year amount left=2*(2*(2*x-65)-65)-65=8*x-(2^3-1)*65
after fourth year amount left=2*(8*x-7*65)-65
similarly after nth year amount left=(2^n)*x-(2^n-1)*65
after Sixth year amount is =0;
(2^6)*x-(2^6-1)*65=0;
From this x=63.984375
clearly from the answer this is impossible in practical world.

Let us suppose no of head occurences be x and number of tail ocurrennces will be 20-x ;since total no of throws is20,
now according to question it is given that for each head  one of the freinds gains $2 so total gain is 2*x.Similarly total loss is 3*(20-x).
also 2*x=3*(20-x)8
From the equation x=12.
Therefore number of heads is 12 and number of tails is 8