# 2.1: Budgeting

- Page ID
- 88475

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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)In this section, you will learn to:

- Use terms associated with finances (expenses, bills, income, budget, taxes, checking account, savings account etc.)
- Understand the connection between investing and borrowing

So that they can produce a budget with a net positive balance.

Throughout this chapter, we will discuss the definitions and formulas associated with finances. Many of these definitions and formulas are covered in all types of mathematics courses at the college level; however, understanding the mathematics behind these concepts and how they apply to your everyday life are two very different ideas. As you go through this section, and this chapter for that matter, consider how these ideas apply to your own life. Have you ever made a budget? What comes to mind when you think of the differences between income and expenses? When/where do you see yourself investing money? What about borrowing? Review the following definitions and try to name examples of each in your own life.

**Income:**This is money received, usually on a regular basis. Income can be from work or through investments.**Expense:**This is money spent on something. Some expenses may be reoccurring, others may be one-time expenses.**Budget:**An estimate of expected income and expenses for a set period of time.**Taxes:**A obligatory contribution to state and federal revenue, imposed by the government on workers' income and business profits, or added to the cost of some goods, services, and transactions.

It is vital that your income (after taxes) meets, and ideally exceeds, your expenses; in other words, you should try to create a budget with a net positive balance. You can do this is in any time period you would like (e.g Bi-Weekly, Monthly, or Yearly). In the case of budgeting, planning around your income schedule is helpful; having a weekly, or biweekly, budget with a net positive balance will grow monthly and yearly.

In order to create a budget, you should list your income and expenses. Although you can do this in any way that you would like, we'll recommend that you use technology (Google Sheets or Microsoft Excel) to help.

- Make a list of your income (after taxes).
- Identify your reoccurring expenses. Be sure to include everything you can here! (Bills, Food, Subscriptions, etc.)
- Determine whether your income exceeds your expenses.
- If your income does not exceed your expenses, determine whether there are any expenses you can cut back on; if not, determine how you can increase your income.

It may not be easy to do this process on the first try! Sometimes it takes a couple of months of tracking to nail your budget down. With your Office 365 account, you can use this Personal Monthly Budget spreadsheet to enter your projected budget; then at the end of the month, you can come back and enter your actual budget to compare the difference! This information should be used to plan for future months and examine your spending habits.

There are many budgeting guidelines that can be found online, but sources like Nerdwallet offer a simple budgeting framework called the 50/30/20 rule where 50% of your monthly income goes directly to your needs, 30% of your income goes to your wants, and the last 20% of your income goes to savings and debt repayment; note the savings and debt repayment category can be any payments towards loans that would be considered additional payments as well as building an emergency fund/setting aside money for retirement.

Now that you have an idea of what your finances look like, let's review a couple more financial tools that we can use for our benefit.

**Checking Account:**An account at a bank that allows checks to be drawn by the depositor. Since this account is more fluid, no interest is given on money kept here. Online payment systems like Venmo and PayPal aren't technically checking accounts, but they do operate in a similar manner.**Savings Account:**An account at a bank that earns interest.**Investments:**Money spent with an expectation of profit or material result.**Loans:**A sum of money that is borrowed and expected to be paid back (usually with interest).

Ideally, you've got some leftover money each day, week, month, or year. If so, what will you be doing with it? Putting it into the bank? Investing it somewhere? If not, how will you be dealing with the negative balance? Loans may be an option, but as we'll explore this chapter, interest (simple or compound) can increase the severity of the situation!

### Net Positive Balance

In order for your budget to have a net positive balance, your income must exceed your expenses. Taking the sum of your expenses will help you determine the minimum amount of income you need to make a net positive balance.

Given Joseph's expenses below, determine the minimum income needed in order for Joseph to have a net positive budget.

Item | Cost |
---|---|

Food | $400 |

Housing | $600 |

Transportation | $300 |

Entertainment | $80 |

Miscellaneous | $310 |

Gas | $120 |

Phone | $70 |

Electricity | $45 |

Utilities | $85 |

###### Solution

Adding up Joseph's expenses for Food, Housing, Transportation, Entertainment, Miscellaneous, Gas, Phone, Electricity, and Utilities, we get

This means Joseph should plan to have an income that exceeds \($2010\) if they want to have a budget with a net positive balance.

### Budgeting for Specific Expenses

Budgeting is necessary at a micro and macro level. Once you've established a monthly budget, you'll need to adjust it for various life events. How does family planning play a role in your budget? What if you're planning a trip or vacation? We can identify how much we need to budget for such things, by identifying as much of the costs as possible.

A couple is getting ready to drive across the USA from Philadelphia, PA to Los Angeles, CA in five days. The distance is approximately \( 3,000 \) miles. The average price of gasoline is about \( $2.00 \) per gallon. They plan to stay in a hotel for four nights and budget for the cost of meals to be about \($50\) per day per person.

- If their van averages \(25\) mpg, estimate the total cost of the gas for the trip. Round to the nearest whole number.
- b) If the average cost of a hotel stay per night is about \($85\) plus \(18%\) hotel tax, determine the total cost for hotels for their trip. Round answer to the nearest whole number.
- How much should they budget for the total cost of meals for their trip?

###### Solution

- Since the trip is approximately \(3000\) miles and the van gets an average of \(25\) mpg, the couple should expect to use \(\dfrac{3000}{25}=120\) gallons of gas. If the cost of gas is \($2.00\) the total expected cost of gas for the trip is \(120\cdot2\)=\($240\).
- Now, if the average cost of the hotel stay per night is about \($85\) plus \(18%\) hotel tax, we can say the expected cost of the hotels for \(4\) nights (before tax) is \(4\cdot85=$340\). Then, the \(18%\) tax on the \(4\) nights is \(340⋅0.18=$61\). Adding these totals together we get that the total expected cost is \(340+61=$401\). Note: The alternative way to find this value would be to multiply the \(4\)-night total times 1.18 (the total stay with 18% tax included) so that \(340\cdot1.18=$401\).
- Finally, since the couple will be staying in a hotel for \(4\) nights, the trip will take \(5\) days. With the cost of meals being about \($50\) per day per person, the couple must budget \($100\) total for the two of them each day. Multiplying \(5\) days times \($100\) for each day gives us a total of \($500\) to be budgeted for meals.

This means that the couple can expect the total trip to cost about \($240 +$401+$500=$1,141\).