well since you sponsored a website i think its effect will be a little late first the creator of that theme he should submit them to lots of free wp themes websites like 100+ including those which have are high on google search results
then if the website you sponsered is really cool
you might get 2 or 3 downloads after that if they add this theme on their blog
now since you sponsored the theme for backlinks it will take lots of time
as the website which have you theme are new and with time when they will grow and get some pr then only it will effect you website
so i think results are permanent and worth $40 if you can wait that much
may be it affect after atleast 6 month
and after you theme is liitle old on free theme website and no of downloads increases, you get more downloads as you theme is on top 10 list and more people add it
so it continues this way but if you are expecting a good in result in less time then thats not going to happen
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