This is a retirement model which models salary with both a constant growth rate for cost of living raises as well as regular salary increases for promotions. The model is broken up into the following sections:
from dataclasses import dataclass
import numpy_financial as npf
All of the inputs for the model are defined here. A class is constructed to manage the data, and an instance of the class containing the default inputs is created.
@dataclass
class ModelInputs:
starting_salary: int = 60000
promos_every_n_years: int = 5
cost_of_living_raise: float = 0.02
promo_raise: float = 0.15
savings_rate: float = 0.25
interest_rate: float = 0.05
annual_cash_spend: int = 40000
years_in_retirement: int = 25
model_data = ModelInputs()
model_data
# Output of the calculation
ModelInputs(starting_salary=60000, promos_every_n_years=5, cost_of_living_raise=0.02, promo_raise=0.15,
savings_rate=0.25, interest_rate=0.05, annual_cash_spend=40000, years_in_retirement=25)
d2 = ModelInputs(starting_salary=40000)
#This is why to use data = model_data. More flexibility
d2
# Output of the calculation
ModelInputs(starting_salary=40000, promos_every_n_years=5, cost_of_living_raise=0.02, promo_raise=0.15,
savings_rate=0.25, interest_rate=0.05, annual_cash_spend=40000, years_in_retirement=25)
Here the salary for each year is calculated. We assume that the salary grows at a constant rate each year for cost of living raises, and then also every number of years, the salary increases by a further percentage due to a promotion or switching jobs. Based on this assumption, the salary would evolve over time with the following equation:
$$s_t = s_0 (1 + r_{cl})^n (1 + r_p)^p$$
Where:
And in Python format:
def salary_at_year(data,year):
"""
Gets the salary at a specified year using promotions and cost of living raise
"""
#There is a promotion every n years, here we find out how many promotions would happen in those years
num_promos = int(year / data.promos_every_n_years) #int to remove decimal
#This is the above formula in python
salary_t = data.starting_salary * (1 + data.cost_of_living_raise)**year * (1 + data.promo_raise)**num_promos
return salary_t
Salary at year function returns the salary at different specified years. Below uses a loop to specify the growth at each year. These will be useful later when this function is used in the Wealths section of the model
for year in range(1,7):
salary = salary_at_year(model_data, year)
print(f'The salary at year {year} is ${salary:,.0f}.')
# Output of the calculation
The salary at year 1 is $61,200.
The salary at year 2 is $62,424.
The salary at year 3 is $63,672.
The salary at year 4 is $64,946.
The salary at year 5 is $76,182.
The salary at year 6 is $77,705.
Using the default inputs, the salary increases at 2% per year until year 5, where a promotion occurs and there's a larger jump in salary.
The wealths portion of this model deals with adding the savings rate to the salary calculated in the Salaries section. This is used to calculate cash saved and applying the investment rate (interest) to the accumulated wealth.
To calculate cash saved, it is simply:
$$c_t = s_t * r_s$$
Where:
def cash_saved_during_year(data,year):
"""
Calculating cash saved for a given year using the salary at that year * the savings rate
"""
salary = salary_at_year(data,year)
cash_saved = salary * data.savings_rate
return cash_saved
To get the wealth at each year, it is just applying the investment return to last year's wealth, then adding this year's cash saved:
$$w_t = w_{t-1} (1 + r_i) + c_t$$
Where:
def wealth_at_year(data,year,prior_wealth):
"""
This calculates the accumulated wealth for a given year using prior years wealth,
interest, and cash saved during that year.
"""
cash_saved = cash_saved_during_year(data,year)
wealth = prior_wealth * (1 + data.interest_rate) + cash_saved
return wealth
Again, just like in the Salaries section, we can now get the output for each year, but we don't know ultimately how many years we will have to run it. That will be determined in the Retirement section. So for now, just the first few years of wealth accumulation is shown:
prior_wealth = 0 # Starting with zero saved cash
for year in range(1,7):
wealth = wealth_at_year(model_data,year,prior_wealth)
print(f'The wealth at year {year} is ${wealth:,.0f}')
#Setting next years prior wealth to this year's wealth
prior_wealth = wealth
# Output of the calculation
The wealth at year 1 is $15,300
The wealth at year 2 is $31,671
The wealth at year 3 is $49,173
The wealth at year 4 is $67,868
The wealth at year 5 is $90,307
The wealth at year 6 is $114,248
Assuming default inputs, the wealth is going up about 25% of the salary each year, plus the interest. At year 6, the amount grows more significantly due to the promotion.
This section of the model includes everything and returns the final answer. It uses the wealths at each year and salaries from each year to track the wealth overtime until it hits the retirement cash goal. Once the wealth is bigger than the cash goal, they can retire. The retirement cash goal is calculated using annual retirement cash spend and projected years in retirement.
def desired_cash(data):
"""
Using the numpy_financial Present Value function, desired cash is calculated with the
interest rate, projected years in retirement and projected annual cash in retirement
"""
cash_goal= npf.pv(data.interest_rate,data.years_in_retirement,-data.annual_cash_spend,0)
return cash_goal
def years_to_retirment(data):
#Zero cash is saved and the year here will be the first in the loop.
prior_wealth = 0
wealth = 0
year = 0
print('Wealths over time:')
while wealth < desired_cash(model_data):
year = year + 1
wealth = wealth_at_year(data, year, prior_wealth)
print(f'The wealth at year {year} is ${wealth:,.0f}')
#Next years prior wealth to this year's wealth
prior_wealth = wealth
#Outside of the while loop. Wealth must be greater than desired cash.
# The final year used must be the years until retirement.
print(f'\n\nRetirement:')
print(f'It will take {year} years to retire')
return year
ytr = years_to_retirment(model_data)
# Output of the calculation
Wealths over time:
The wealth at year 1 is $15,300
The wealth at year 2 is $31,671
The wealth at year 3 is $49,173
The wealth at year 4 is $67,868
The wealth at year 5 is $90,307
The wealth at year 6 is $114,248
The wealth at year 7 is $139,775
The wealth at year 8 is $166,975
The wealth at year 9 is $195,939
The wealth at year 10 is $229,918
The wealth at year 11 is $266,080
The wealth at year 12 is $304,542
The wealth at year 13 is $345,431
The wealth at year 14 is $388,878
The wealth at year 15 is $439,025
The wealth at year 16 is $492,294
The wealth at year 17 is $548,853
The wealth at year 18 is $608,878
Retirement:
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