Most direct route

Rio to Belo Horizonte - 7hrs $12 - stop at Ouro Preto?

Belo Horizonte to Brasilia - 12hrs $30

Brasilia to Cuiaba - 18hrs $27

Cuiaba to Porto Velho - 24hrs $22

Porto Velho to Rio Branco - 7hrs $17

Rio Branco to Assis Brasil - 6hrs $8.50

Assis Brasil to Inapari (Peru), on to Iberia, then Puerto Maldonado and Cuzco or Lima :)

[Boat from Porto Velho to Manaus - 3 days ~$40
Highway to Manaus is impassable past Humaita :)]

Total from Rio de Janeiro to Assis Brasil (direct) - $116.50  ¶ 7:43 AM