How to do range grouping on a column using dplyr?

I want to group a data.table based on a column's range value, how can I do this with the dplyr library?

For example, my data table is like below:

library(data.table)
library(dplyr)
DT <- data.table(A=1:100, B=runif(100), Amount=runif(100, 0, 100))

Now I want to group DT into 20 groups at 0.05 interval of column B, and count how many rows are in each group. e.g., any rows with a column B value in the range of [0, 0.05) will form a group; any rows with the column B value in the range of [0.05, 0.1) will form another group, and so on. Is there an efficient way of doing this group function?

Thank you very much.

-----------------------------More question on akrun's answer. Thanks akrun for your answer. I got a new question about the "cut" function. If my DT is like below:

DT <- data.table(A=1:10, B=c(0.01, 0.04, 0.06, 0.09, 0.1, 0.13, 0.14, 0.15, 0.17, 0.71)) 

by using the following code:

DT %>% 
  group_by(gr=cut(B, breaks= seq(0, 1, by = 0.05), right=F) ) %>% 
  summarise(n= n()) %>%
  arrange(as.numeric(gr))

I expect to see results like this:

          gr n
1   [0,0.05) 2
2 [0.05,0.1) 2
3 [0.1,0.15) 3
4 [0.15,0.2) 2
5 [0.7,0.75) 1

but the result I got is like this:

          gr n
1   [0,0.05) 2
2 [0.05,0.1) 2
3 [0.1,0.15) 4
4 [0.15,0.2) 1
5 [0.7,0.75) 1 

Looks like the value 0.15 is not correctly allocated. Any thoughts on this?

We can use cut to do the grouping. We create the 'gr' column within the group_by, use summarise to create the number of elements in each group (n()), and order the output (arrange) based on 'gr'.

library(dplyr)
 DT %>% 
     group_by(gr=cut(B, breaks= seq(0, 1, by = 0.05)) ) %>% 
     summarise(n= n()) %>%
     arrange(as.numeric(gr))

As the initial object is data.table, this can be done using data.table methods (included @Frank's suggestion to use keyby)

library(data.table)
DT[,.N , keyby = .(gr=cut(B, breaks=seq(0, 1, by=0.05)))]

EDIT:

Based on the update in the OP's post, we could substract a small number to the seq

lvls <- levels(cut(DT$B, seq(0, 1, by =0.05)))
DT %>%
   group_by(gr=cut(B, breaks= seq(0, 1, by = 0.05) -
                 .Machine$double.eps, right=FALSE, labels=lvls)) %>% 
   summarise(n=n()) %>% 
   arrange(as.numeric(gr))
#          gr n
#1   (0,0.05] 2
#2 (0.05,0.1] 2
#3 (0.1,0.15] 3
#4 (0.15,0.2] 2
#5 (0.7,0.75] 1