def apr
      payment_ratio = self.monthly_payment_with_fees / self.loan_amount
      f             = lambda { |k| (k**(self.period + 1) - (k**self.period * (payment_ratio + 1)) + payment_ratio) }
      f_deriv       = lambda { |k| ((self.period + 1) * k**self.period) - (self.period * (payment_ratio + 1) * k**(self.period - 1)) }

      root = newton_raphson(f, f_deriv, self.monthly_interest_rate + 1)
      100 * 12 * (root - 1).to_f
    end
def apr
      payment_ratio = self.monthly_payment_with_fees / self.loan_amount
      f             = lambda { |k| (k**(self.period + 1) - (k**self.period * (payment_ratio + 1)) + payment_ratio) }
      f_deriv       = lambda { |k| ((self.period + 1) * k**self.period) - (self.period * (payment_ratio + 1) * k**(self.period - 1)) }

      root = newton_raphson(f, f_deriv, self.monthly_interest_rate + 1)
      100 * 12 * (root - 1).to_f
    end
def apr payment_ratio = self . monthly_payment_with_fees / self . loan_amount f = lambda { | k | ( k ** ( self . period + 1 ) - ( k ** self . period * ( payment_ratio + 1 ) ) + payment_ratio ) } f_deriv = lambda { | k | ( ( self . period + 1 ) * k ** self . period ) - ( self . period * ( payment_ratio + 1 ) * k ** ( self . period - 1 ) ) } root = newton_raphson ( f , f_deriv , self . monthly_interest_rate + 1 ) 100 * 12 * ( root - 1 ) . to_f end
solves APR
 [a (1 + a)^N] / [(1 + a)^N - 1] - P/C = 0
 where a = APR/1200, N = period, P = monthly payment, C = loan_amount
 calculate APR uses the Newton-Raphson to find the root (the value for 'a' that makes f(a) = 0)
solves APR [ a ( 1 + a ) ^N ] / [ ( 1 + a ) ^N - 1 ] - P / C = 0 where a = APR / 1200 N = period P = monthly payment C = loan_amount calculate APR uses the Newton - Raphson to find the root ( the value for a that makes f ( a ) = 0 )