I believe OP is saying the difference is equal to, not that the difference is caused by.
USA GDP PPP per capita in 2018 according to the IMF: $62606
Mexico, ditto: $20602
20602×1.01^100 = 55724.6
The difference is closer to 1.1177% compounded over a century, but I wouldn’t quibble over the extra digits when most news reports of economic growth are rounded to the nearest 0.25%.
World bank data seems to differ:
https://data.worldbank.org/indicator/NY.GDP.MKTP.KD.ZG?locat...