Bausparen-with-Friends

I am a Graph-of-a-Function, that shows the Concept of a Bausparvertrag, where the avarage Wait-Time can be reduced, when Friends pool their Money.

Observations

The average Wait-Time can be reduced from 10 Years to 5,5 Years.
The Minimum of the Example is reached already with 10 Friends.
Because of the used Granularity of one Year, the Function sometimes also goes up.

The corresponding Background-Story is explained in the Blog-Entry Bauuuspaaarvertrag of the Project-Blog.

Program

The following Python-Program has been used to generate the Function-Graph:

import matplotlib.pyplot as Plt

# Define Constants
COSTS_PER_HOUSE      = 100000 # We can buy a House for 100.000 Coins
MONEY_PER_YEAR       = 10000  # Every Friend can save 10.000 Coins each Year
MAXIMUM_YEAR_COUNT   = 10     # In 10 Years all Houses are built
MAXIMUM_FRIEND_COUNT = 50     # Maximum Number of Friends that pool the Money

# Calculate the Sum of Years to buy all Houses
def Calculate_Wait_Time_Sum(Friends_Count):
        Wait_Time_Sum = 0
        Saved_Money = 0
        Houses = 0
        # Let's see, what we can build in 10 Years
        for Year in range(1, MAXIMUM_YEAR_COUNT + 1):
                # Calculate the saved Money per Year
                Saved_Money += Friends_Count * MONEY_PER_YEAR
                # Buy Houses with the saved Money
                while Saved_Money >= COSTS_PER_HOUSE:
                        Houses += 1
                        Saved_Money -= COSTS_PER_HOUSE
                        Wait_Time_Sum += Year
                        print(f" House %2d bought after %2d Years" % (Houses, Year))
        return Wait_Time_Sum

def Print_Results_Graph():
        # Lists for Data
        Friends_Count_List = []      # X-Axis
        Average_Wait_Years_List = [] # Y-Axis
        # Generate Data
        for Friends_Count in range(1, MAXIMUM_FRIEND_COUNT + 1):
                Friends_Count_List.append(Friends_Count)
                Average_Wait_Years = Calculate_Wait_Time_Sum(Friends_Count) / Friends_Count
                Average_Wait_Years_List.append(Average_Wait_Years)
        # Plot Data
        Plt.plot(Friends_Count_List, Average_Wait_Years_List)
        Plt.xlabel('Number of Friends')
        Plt.ylabel('Average Years to wait')
        Plt.title('Bausparen with Friends')
        Plt.savefig("Bausparen-With-Friends.png", format="png", dpi=300)
        Plt.show()

Print_Results_Graph()