Generate data from truncated normal distribution with exact mean and sd in R

I struggle with the following task: I need to generate data from a truncated normal distribution. The sample mean and standard deviation should match exactly those specified in the population. This is what I have so far:

    mean <- 100
    sd <- 5
    lower <- 40
    upper <- 120
    n <- 100   

    library(msm)    
    data <- as.numeric(mean+sd*scale(rtnorm(n, lower=40, upper=120)))

The sample that's created takes on exactly the mean and sd specified in the population. But some values exceed the intended bounds. Any idea how to fix this? I was thinking of just cutting off all values outside these bounds, but then mean and sd don't resemble those of the population anymore.