It’ll become greater after 12 applications:

1. For 11 times 1.25¹¹ ≈ 11.64 < 12 = 1+ 1×11
2. For 12 times 1.25¹² ≈ 14.55 > 13 = 1 + 1×12

There’s no need for a precise solution since it’s integers anyway.