Sarafina is making monthly payments into an annuity. she wants to have $400 in the fund to buy a new convection range in nine months, and the account pays 4.8% annual interest. what are her monthly payments to the account?

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.