MIT Intro to CS and Programming PS1A

This is the solution to problemset1 question A of 6.0001 entitled Introduction to Computer Science and Programming in Python (Fall 2016).

Part A: House Hunting You have graduated from MIT and now have a great job! You move to the San Francisco Bay Area and decide that you want to start saving to buy a house.  As housing prices are very high in the Bay Area, you realize you are going to have to save for several years before you can afford to make the down payment on a house. In Part A, we are going to determine how long it will take you to save enough money to make the down payment given the following assumptions:

1. Call the cost of your dream home total_cost. 
2. Call the portion of the cost needed for a down payment portion_down_payment. For simplicity, assume that portion_down_payment = 0.25 (25%). 
3. Call the amount that you have saved thus far current_savings. You start with a current savings of $0. 
4. Assume that you invest your current savings wisely, with an annual return of r (in other words, at the end of each month, you receive an additional current_savings*r/12 funds to put into your savings – the 12 is because r is an annual rate). Assume that your investments earn a return of r = 0.04 (4%). 
5. Assume your annual salary is annual_salary. 
6. Assume you are going to dedicate a certain amount of your salary each month to saving for the down payment. Call that portion_saved. This variable should be in decimal form (i.e. 0.1 for 10%). 
7. At the end of each month, your savings will be increased by the return on your investment, plus a percentage of your monthly salary (annual salary / 12).

Write a program to calculate how many months it will take you to save up enough money for a down payment. You will want your main variables to be floats, so you should cast user inputs to floats.    1 Your program should ask the user to enter the following variables:

1. The starting annual salary (annual_salary)
2. The portion of salary to be saved (portion_saved)
3. The cost of your dream home (total_cost)

Hints To help you get started, here is a rough outline of the stages you should probably follow in writing your code:

• Retrieve user input. Look at input() if you need help with getting user input. For this problem set, you can assume that users will enter valid input (e.g. they won’t enter a string when you expect an int)
• Initialize some state variables. You should decide what information you need. Be careful about values that represent annual amounts and those that represent monthly amounts.

Try different inputs and see how long it takes to save for a down payment.  Please make your program print results in the format shown in the test cases below.    

Test Case 1

>>>

Enter your annual salary: 120000

Enter the percent of your salary to save, as a decimal: .10

Enter the cost of your dream home: 1000000

Number of months: 183  

>>>

Test Case 2

>>>

Enter your annual salary: 80000  

Enter the percent of your salary to save, as a decimal: .15

Enter the cost of your dream home: 500000

Number of months: 105

>>>

(Bell, Grimson & Guttag, 2016)

The first thing you need to do in order to solve this problem is to read through the variables very carefully to ensure that you have everything set up properly.

Once you have the values you can set up a while loop that stops once the once the savings is greater than the deposit. You are going to need to add up the amount of money that is being saved as well as the return that you are making on the investment.

The return they are looking for is the number of months which you can keep track of with a simple counter.

Solution

annual_salary = float(input("Enter your annual salary: "))

portion_saved = float(input("Enter the percent of your salary to save, as a decimal: "))

total_cost = float(input("Enter the cost of your dream home: "))

portion_down_payment = total_cost * 0.25

current_savings = 0

r = 0.04

months = 0

while current_savings < portion_down_payment:

   current_savings += (annual_salary/12)*portion_saved + current_savings*(r/12)

   months += 1

print("Number of months: ", months)

Output

Test Case 1

Enter your annual salary: 120000

Enter the percent of your salary to save, as a decimal: .10

Enter the cost of your dream home: 1000000

Number of months:  183

Test Case 2

Enter your annual salary: 80000

Enter the percent of your salary to save, as a decimal: .15

Enter the cost of your dream home: 500000

Number of months:  105

Reference
Ana Bell, Eric Grimson, and John Guttag. 6.0001 Introduction to Computer Science and Programming in Python. Fall 2016. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu. License: Creative Commons BY-NC-SA.