Save For Your Retirement!

Retirement Age:

Estimate the age at which you want to retire. Store this in a variable called retirementAge.

In [ ]:

retirementAge = 70

Estimate how long you think you'll live. Assume that is after your retirement age. Store this in a variable called deathAge.

In [ ]:

deathAge = 85

Retirement Pay:

Figure out how much income you want to live on during your retirement. Assume for simplicity there is no inflation so you can use 2020 dollars. Store this in a variable called retirementPay.

In [ ]:

retirementPay = 50000

Retirement Savings

Figure out how much you need to retire by using the formula savings = (deathAge - retirementAge)*retirementPay

In []: savings = (deathAge - retirementAge)*retirementPay

print(savings)

How to Build Up Your Retirement Savings

Assume in one more year you have your dream job and are making a decent salary, which you will make until you retire.

Every year you put in M dollars into the stock market, which earns R rate of return each year.

Your retirement account then grows in the following pattern.

• After Year 1, you'll have M in your account
• After Year 2, you'll have M*(1+R) + M in your retirement account.
• After Year 3, you'll have M*(1+R)**2 + M*(1+R) + M
• After Year 4, you'll have M*(1+R)**3 + M*(1+R)**2 + M*(1+R) + M
• After Year 5, you'll have M*(1+R)**4 + M*(1+R)**3 + M*(1+R)**2 + M*(1+R) + M

In general, if you work W years, you should have

(1+)+(1+)1++M(1+R)W+M(1+R)W1++M

in your retirement savings account.

Find M for various values of R

Assuming R=.05 is the average annual return on the stock market, and you work W=retirementAge - currentAge number of years, how large does M need to be in order for you to have savings?

Repeat this exercise for

• R = .07
• R = .10

(python)Question 3

Customize the code below for your age and produce plots for the three cases of

• =.05
• =.07
• =.1

Change the code below and create separate code cells for your 3 different plots. 1 point for each plot!

In [1]:

currentAge= 34

W = retirementAge - currentAge

R =.05

x = 1 +R

M = savings/((1-x**W)/(1-x)) ## This is the formula we derived in class. 

## Alternatively a linear search approach can be implemented

print(M)

def total_savings(returnRate,numYears,totalSavings): """Assumes returnRate is a float between 0 and 1. numYears is the number of years until retirement. totalSavings is the amount you need to save. returns the yearly investment amount.""" myInvestment = 0 myTotal = 0 while myTotal < totalSavings: mytotal = 0 for i in range(1,numYears+1): mytotal= mytotal + myInvestment*(1+returnRate)**(i-1) if mytotal < totalSavings: mytotal =0 else: myTotal = mytotal myInvestment += 1 return myInvestment

Plot your savings growth!

Now import matplotlib.pyplot in order to plot the growth of your portfolio.

import matplotlib.pyplot as plt

mySavings = [] for i in range(0,W+1): if i ==0: mySavings.append(0) else: mySavings.append(M + mySavings[-1]*(1 + R))

fig = plt.figure() plt.plot(mySavings) plt.title('Retirement Savings at 50%') plt.xlabel('Number of years working') plt.ylabel('Value of Retirement Account ($)')