Why can't you sum a float column? float is a numeric data type and it can be used in SUM().
Here's what I used to test.
DECLARE @Appllication TABLE(
IDint,
Datedate,
Costfloat,
Fundingfloat
)
INSERT INTO @Appllication
VALUES
(1,'20140201', 10.52, 5),
(1,'20140202', 20, 15),
(3,'20140205', 30.1245, 50),
(3,'20140201', 110, 5)
select ID, MAX(Date) Date, SUM(Cost) Cost, MAX(Funding) Funding from @Appllication
group by ID