You can find the AMA dues policy in their PDF library here:
http://modelaircraft.org/files/912.pdf
Here's a quick breakdown of the important part of that document that applies to you:
FIRST QUARTER: If you join AMA as a first time, new member from
January 1st through March 31st, you will do so at the full, open rate.</p>
SECOND QUARTER: If you join AMA as a first time, new member from
April 1st through June 30th, you will pay the full, open rate. The
Following year, your renewal notice will reflect a 25% reduction in dues.</p>
THIRD QUARTER: If you join AMA from July 1st through September
15th, you will pay the full, open rate. The following year, your
renewal notice will reflect a 50% reduction in dues.</p>
FOURTH QUARTER: If you join AMA from September 16th through
December 31st, you will pay the full open rate. You will receive
membership for the remainder of that year, plus membership for the
following year.
Basically, if you join now you pay the full rate of $58. But next years dues will be only have of the regular rate. But if you wait until after September 1st then you will pay $58 and that will include the rest of this year AND next year as well.
Ken</p>