The Gades Foundation and HBM Corporation are eager to donate generously to their favorite charities.
The Gades Foundation donated \$250$250dollar sign, 250 in the first month, and each month afterward their cumulative donation total increases by \$100$100dollar sign, 100.
The HBM Corporation donated \$64$64dollar sign, 64 in the first month, and each month afterward their cumulative donation total increases by 75\%75%75, percent.
They started making donations at the same time, and they both make their monthly donations at the beginning of each month.
What is the first month in which HBM Corporation's cumulative donation total exceeds the Gades Foundations' cumulative total?