This question seems to forget HKB’H’s role in this world.
The rich person is not able to ‘buy himself a place in oilom habo’ any more than the poor man. Rather, he has been given an opportunity to earn his oilom habo in this way, whilst the poor man is given different opportunities to do so.
Do you question how come the rich man does not get the opportunity to ‘buy a place in oilom habo’ by serving Hashem in his destitution?
“Hillel mechayev es ha aniyim, R. Eliezer mechayev es ha ashirim.”
BTW – what makes you think its easier for the rich person to give away $100,000 than for the poor person to give $1,750. Yesh loi moneh, roitzeh mosayim…