Assume that the DPI of a $10-$year fund at the end of its $4$th year is $1\mathrm{.}2$x and that, by that time, $$160$ million of its $$240$ million committed capital has been called. The fund follows a standard $2/20$ fee structure $($European way$).$ What has been the total amount of distributions by the fund by the end of its $4$th year?