Assuming you hold a U.K. passport: $30 for the first month and $5 per month, for the remaining months - add on your card fee of 55tl and it works out around 293tl at today's rates.
Obviously, if your Turkish isn't sufficient to cope with the process then you will need a translator, or a friend who speaks Turkish.
Those figures are as of last month in Istanbul, so a bit cheaper than my guesstimate of 300tl.
JF