The Excel PMT function

PMT_function.rb

module Excel
  module Formulas  
    ## rate = The interest rate, per period.
    ## nper = The number of periods over which the loan or investment is to be paid.
    ## pv = The present value of the loan / investment.
    ## fv = An optional argument that specifies the future value of the loan / investment, at the end of nper payments. If omitted, [fv] has the default value of 0.
    ## type = An optional argument that defines whether the payment is made at the start or the end of the period. 0 for the payment is made at the end of the period and 1 for the payment is made at the beginning of the period. If the type argument is omitted, it takes on the default value of 0 (denoting payments made at the end of the period).
    
    ## Eg 1. pmt(0.0199, 1, 100) => tax of 1.99% in the 1 parcel of $100 ~= $101.99 with $1.99 tax
    ## Eg 2. pmt(0.0199, 2, 100) => tax of 1.99% in the 2 parcels of $100 ~= $51.50 with $1.5 tax per parcel 
    ## Eg x. pmt(0.0199, x, 100) => tax of 1.99% in the x parcels of $100 ~= ∞
    
    def pmt(rate, nper, pv, fv=0, type=0)
      ((pv * pvif(rate, nper) - fv ) / ((1.0 + rate * type) * fvifa(rate, nper)))
    end

    protected
    
    def pow1pm1(x, y)
      (x <= -1) ? ((1 + x) ** y) - 1 : Math.exp(y * Math.log(1.0 + x)) - 1
    end
    
    def pvif(rate, nper)
      (rate.abs > 0.5) ? ((1 + rate) ** nper) : Math.exp(nper * Math.log(1.0 + rate))
    end
  
    def fvifa(rate, nper)
      (rate == 0) ? nper : pow1pm1(rate, nper) / rate
    end
    
  end
end