solution.py

# Let us begin with an example:

# A man has a rather old car being worth $2000.
# He saw a secondhand car being worth $8000.
# He wants to keep his old car until he can buy the secondhand one.

# He thinks he can save $1000 each month but the prices of his old car
# and of the new one decrease of 1.5 percent per month.
# Furthermore this percent of loss increases of 0.5 percent at the end of every two months.
# Our man finds it difficult to make all these calculations.

# Can you help him?
# How many months will it take him to save up enough money to buy the car he wants,
# and how much money will he have left over?

# Parameters and return of function:
# parameter (positive int or float, guaranteed) startPriceOld (Old car price)
# parameter (positive int or float, guaranteed) start_price_new (New car price)
# parameter (positive int or float, guaranteed) save_per_month
# parameter (positive float or int, guaranteed) percent_loss_by_month

# nbMonths(2000, 8000, 1000, 1.5) should return [6, 766] or (6, 766)

# Detail of the above example:
# end month 1: percentLoss 1.5 available -4910.0
# end month 2: percentLoss 2.0 available -3791.7999...
# end month 3: percentLoss 2.0 available -2675.964
# end month 4: percentLoss 2.5 available -1534.06489...
# end month 5: percentLoss 2.5 available -395.71327...
# end month 6: percentLoss 3.0 available 766.158120825...
# return [6, 766] or (6, 766)

# where 6 is the number of months at the end of which he can buy the new car and 766
# is the nearest integer to 766.158... (rounding 766.158 gives 766).


def nbMonths(start_price_old, start_price_new, save_per_month, percent_loss_by_month):
    months = 0
    total_sum = start_price_old

    while total_sum < start_price_new:
        months += 1
        if not months % 2:
            percent_loss_by_month += 0.5

        start_price_old *= (100 - percent_loss_by_month) / 100
        start_price_new *= (100 - percent_loss_by_month) / 100

        total_sum = start_price_old + save_per_month * months

    return [months, round(total_sum - start_price_new)]