This can be done by the following formula (lengthy as you need to round each step of the way)
=ROUNDDOWN(SUM(A1:A5),0)+IF(ROUND(SUM(A1:A5)-ROUNDDOWN(SUM(A1:A5),0),2)<=0.12,0,IF(ROUND(SUM(A1:A5)-ROUNDDOWN(SUM(A1:A5),0),2)<=0.37,0.25,IF(ROUND(SUM(A1:A5)-ROUNDDOWN(SUM(A1:A5),0),2)<=0.63,0.5,IF(ROUND(SUM(A1:A5)-ROUNDDOWN(SUM(A1:A5),0),2)<=0.87,0.75,IF(ROUND(SUM(A1:A5)-ROUNDDOWN(SUM(A1:A5),0),2)>=0.88,1,0)))))