social security plot showing cumulative benefits for different starts crossover point using matplotlib

README.md

simple line plot example using matplotlib

This example shows the cumulative payout of social security using a normalized base value. It can be used to determine the best time to start collecting social security.

Here are some things the graph tells us.

If you believe that social security will remain viable for your entire life and you expect to live past age 79, then it is better to start collecting social security as late as possible (age 70) because it maximizes your cumulative return.

If you believe that social security will remain viable for your entire life and you expect to die before age 75, then it is better to start collecting social security as early as possible (age 62) because it maximizes your cumulative return.

If you believe that social security will not remain viable after you are age 75 or, perhaps 79, then it is better to start collecting social security as early as possible (age 62) because it maximizes your cumulative return.

Run it like this.

git clone https://gist.github.com/f3fd81748b0bcb0a3b033b921e8ee85a.git ssa
cd ssa
pipenv install pylint matplotlib pyqt5
pipenv run ./ssa.py

Note that it assumes you are using a recent version of python3.

You can get console debug messages like this:

DEBUG=1 pipenv run ./ssa.py

This gist was tested on Ubuntu 22.04 and MacOS Ventura 13.1.

ssa.png

ssa.py

#!/usr/bin/env python3
'''
Find SSA crossover point.

% pipenv install pylint matplotlib pyqt5
% pipenv run ./ssa.py
% DEBUG=1 pipenv run ./ssa.py

Built and tested in ubuntu/gnome 22.04 on an old Macbook 2013 laptop.
'''
import os
import matplotlib.pyplot as plt
import numpy as np

DEBUG = int(os.getenv('DEBUG', '0'))


def ssa(base: float=1.0,   # starting (base) renumeration
        ipm: float=0.6666  # interest per month
        ):
    '''SSA plot - annual with crossover'''
    #base = 1  # base rate in dollars
    #interest = 0.6666
    ipa = ipm*12  # interest 
    fac = 1 + ipa / 100.
    end = 25
    ynas = []
    for i in range(9):
        age = 62 + i
        # Note that the following loop is 1 based rather than 0 based
        # because the value is for the end of each year.
        xna = np.array([j+age for j in range(1, 1+end+(9-i))])
        yna = (base * (xna - age))*(fac**i)
        label = f'Age {age}'
        plt.plot(xna, yna, label=label)
        ynas.append(yna)
    if DEBUG:
        for i, arr in enumerate(ynas):
            print(f'yna[{i}]:')
        print(arr)
    yna0 = ynas[0]
    cages = []  # cross over ages
    for i, arr in enumerate(ynas[1:], start=1):
        for j, val in enumerate(arr):
            k = j+i
            if val > yna0[k]:
                age = 62 + k
                cages.append(age)
                if DEBUG:
                    print(f'DEBUG: yna[{i}][{j}]: {val:>5.2f} '
                          f'k={k} yna0[{k}]={yna0[k]} age={age}')
                break

    xminca = min(cages)
    xmaxca = max(cages)
    plt.axvline(x=xminca, color='green', linestyle='dotted', label=f'first crossover {xminca}')
    if xminca < xmaxca:
        plt.axvline(x=xmaxca, color='red', linestyle='dotted', label=f'last crossover {xmaxca}')
    #plt.annotate(f'Cumulative crossover @{xmaxca}', xy=(xmaxca+1, 13))

    plt.xlabel("Recipient Age")
    plt.ylabel('Normalized Cumulative Payout\n'
               f'Assuming a Base Benefit of ${base} per year')  # starting at $1 per year
    plt.title('Social Security Payment Analysis\n'
              f'Assuming {ipa:2.1f}% per month\nfor {end+9-1} years')
    plt.legend()
    plt.show()


def main():
    '''main'''
    ssa()

if __name__ == '__main__':
    main()