Find the lowest possible monthly payment to pay off balance in full with compound interest, recursive solution.

interest_calculator.rb

EPISILON = 0.01 # calculate to the nearest cent

def calculate_balance_remaining_after_year(starting_balance, monthly_payment, annual_interest_rate)
  12.times.reduce(starting_balance) do |balance|
    balance -= monthly_payment
    balance += (annual_interest_rate / 12) * balance
  end
end

def calculate_lowest_payment_within_bounds(starting_balance, annual_interest_rate, lower_bound, upper_bound)
  median_payment = (lower_bound + upper_bound) / 2.0
  
  balance = calculate_balance_remaining_after_year(starting_balance, median_payment, annual_interest_rate)
  
  if balance > EPISILON
    calculate_lowest_payment_within_bounds(starting_balance, annual_interest_rate, median_payment, upper_bound)
  elsif balance < -EPISILON
    calculate_lowest_payment_within_bounds(starting_balance, annual_interest_rate, lower_bound, median_payment)
  else
    median_payment
  end
end

def find_lowest_monthly_payment(starting_balance, annual_interest_rate)
  minimum_monthly_payment = starting_balance / 12.0
  maximum_monthly_payment = calculate_balance_remaining_after_year(starting_balance, 0, annual_interest_rate) / 12.0

  calculate_lowest_payment_within_bounds(
    starting_balance, annual_interest_rate, minimum_monthly_payment, maximum_monthly_payment
  )
end

if __FILE__ == $0 # this just means run this block if we run the file directly
  require 'test/unit'

  class BalanceCalculatorTest < Test::Unit::TestCase
    def test_equal_monthly_payments_with_no_interest
      balance = calculate_balance_remaining_after_year(1200.0, 100.0, 0)
      assert_equal 0, balance
    end

    def test_no_monthly_payments_with_no_interest
      balance = calculate_balance_remaining_after_year(1200.0, 0, 0)
      assert_equal 1200.0, balance
    end

    def test_no_monthly_payments_with_interest
      balance = calculate_balance_remaining_after_year(1200.0, 0, 0.12)
      assert_in_delta 1352.19, balance, 0.01
    end

    def test_equal_monthly_payments_with_interest
      balance = calculate_balance_remaining_after_year(1200.0, 100.0, 0.12)
      assert_in_delta 71.26, balance, 0.01
    end

    def test_overpayment_with_no_interest
      balance = calculate_balance_remaining_after_year(1200.0, 110.0, 0)
      assert_equal -120.0, balance
    end
    
    def test_calculated_lowest_monthly_payment_actually_pays_off_balance_in_full_to_nearest_cent
      starting_balance = 1200.0
      interest_rate = 0.12
      lowest_monthly_payment = find_lowest_monthly_payment(starting_balance, interest_rate)
      balance = calculate_balance_remaining_after_year(starting_balance, lowest_monthly_payment, interest_rate)
      assert_in_delta 0, balance, 0.01
    end
    
    def test_calculated_lowest_monthly_payment_for_large_values
      starting_balance = 320000.0
      interest_rate = 0.2
      lowest_monthly_payment = find_lowest_monthly_payment(starting_balance, interest_rate)
      balance = calculate_balance_remaining_after_year(starting_balance, lowest_monthly_payment, interest_rate)
      assert_in_delta 0, balance, 0.01
    end

    def test_calculated_lowest_monthly_payment_for_katies_inputs_matches_python_result
      starting_balance = 320000.0
      interest_rate = 0.2
      lowest_monthly_payment = find_lowest_monthly_payment(starting_balance, interest_rate)
      balance = calculate_balance_remaining_after_year(starting_balance, lowest_monthly_payment, interest_rate)
      assert_in_delta 0, balance, 0.01
      assert_in_delta 29157.09, lowest_monthly_payment, 0.01
    end
  end
end