Calculate marginal tax rates using R

Question

I\'m writing a function to calculate tax owed given a level of income according to Australia\'s marginal tax rates.

I\'ve written a simple version of the function that r

Answer 1

I slightly changed your brackets and rates parameters. You can solve this problem using a while loop.

income_tax <- function(income,
    brackets = c(18200,37001,80000,180000),
    rates = c(.19,.325,.37,.45))
{
  nbrackets <- length(brackets)  
  if(income<=brackets[1]) 
    return(0)

  i <- 2
  cumtax <- 0
  while(i <= nbrackets) {
    if(income > brackets[i-1] && income < brackets[i]) 
      return(cumtax + rates[i-1]*(income-brackets[i-1]))
    else 
      cumtax <- cumtax + rates[i-1]*(brackets[i]-brackets[i-1])
      i <- i + 1
  }
  # income > brackets[nbrackets]
  cumtax + rates[nbrackets] * (income - brackets[nbrackets]) 
}

incomes <- seq(0,200000,25000)
round(sapply(incomes,income_tax),0)
# [1]     0  1292  7797 15922 24947 34197 43447 52697 63547

Answer 2

I think you're looking for findInterval:

income_tax <- function(income, 
                       brackets = c(0, 18200, 37000, 80000, 180000, 180000),
                       rates = c(0, .19, .325, .37, .45)) {
  bracketInd <- findInterval(income, brackets, all.inside = TRUE)
  plus <- if (bracketInd <= 2) 0 else 
    sum(sapply(bracketInd:3, function(ind) {
      (brackets[ind] - brackets[ind - 1]) * rates[ind - 1] 
    }))
  if (length(plus) == 0) plus <- 0
  tax <- plus + (income - brackets[bracketInd]) * rates[bracketInd]
  return(tax)
}

You just find between each elements your income is, and use that as an index for brackets and the rates. I also added the values as parameters with default values.

Answer 3

Here's a one-liner that does the trick:

income_tax <- 
function(income,
         brackets = c(18200, 37000, 80000, 180000, Inf),
         rates = c(0, .19, .325, .37, .45)) {        
    sum(diff(c(0, pmin(income, brackets))) * rates)
}

Perhaps the easiest way to see how/why it works is to play around with the core bit of logic with some simpler parameters, like this:

brackets <- c(1:5, Inf)

diff(c(0, pmin(.35, brackets)))
## [1] 0.35 0.00 0.00 0.00 0.00 0.00
diff(c(0, pmin(3.9, brackets)))
## [1] 1.0 1.0 1.0 0.9 0.0 0.0
diff(c(0, pmin(99, brackets)))
## [1]  1  1  1  1  1 94