How to change data within a column in a dataset in R

I have created a for loop that goes through each row of a certain column. I want to change the information written in that cell depending on certain conditions, so I implemented an if/else statement.

for(i in 1:dim(cool)[1]){
  if (cool$a[i] < 3) {
    cool$b <- "Low"
  } else if (cool$a[i] >= 3 && school_data2019$Taxable.Income < 4) {
    cool$b <- "Medium"
  } else if (cool$a[i] >= 4 && school_data2019$Taxable.Income < 5){
    cool$b <- "Rich"
  } else if (cool$a[i] >= 5){
    cool$b <- "Very Rich"
  } 
  i <- i + 1
}

However, the current problem is that the data is printing out one specific outcome: Medium.

I tried to combat this problem by exporting using write.csv and importing using read.csv. When I applied the head() function though, I still got Medium for all rows.

Would anyone be able to help with this please?