aggregate data.table to rows of intervals of original values

I have some data.table with an amount column like:

n = 1e5
set.seed(1)

dt <- data.table(id = 1:n, amount = pmax(0,rnorm(n, mean = 5e3, sd = 1e4)))

And a vector of breaks given like:

breaks <- as.vector( c(0, t(sapply(c(1, 2.5, 5, 7.5), function(x) x * 10^(1:4))) ) )

For each interval defined by these breaks, I want to use data.table syntax to:

1. get counts of amount contained
2. get counts of amount equal to or greater than the left bound (basically n * (1-cdf(amount))

For 1, this mostly works, but doesn't return rows for the empty intervals:

dt[, .N, keyby = breaks[findInterval(amount,breaks)] ] #would prefer to get 0 for empty intvl

For 2, I tried:

dt[, sum(amount >= thresh[.GRP]), keyby = breaks[findInterval(amount,breaks)]  ]

but it didn't work because sum is restricted to within the group, not beyond. So came up with a workaround, which also returns the empty intervals:

dt[, cbind(breaks, sapply(breaks, function(x) sum(amount >= x)))] # desired result

So, what's the data.table way to fix my 2. and to get the empty intervals for both?