Cash transfers can help poor families to meet the costs associated with sending their children to school. Demand constraints are a major impediment to schooling attainment in rural areas. Educational grants can contribute to raise schooling attainment in rural areas and thereby to close the gap between educational levels in rural areas and national levels. In 1997, the Mexican government initiated such a program of cash transfers, called PROGRESA, targeted to children living in poor and extremely poor rural regions. The present work shows that the program effectively retains children in school leading to important gains in schooling attainment. The grants succeed at lowering the drop out rates by 30-45\% for the eligible grades of primary and secondary school. On average, the program increases the schooling attainment of the poor by almost 5 months, from 6.9 years to 7.4 years. Moreover, the program successfully reaches the poorest and benefits them most. Children from the second lowest well-being quintile, as measured by a poverty index, are the ones that gain most from the program, along with children of uneducated parents. Finally, relaxing demand constraints with some financial help counters effectively the school accessibility constraints at the secondary school level.