Financial Maths: Plan and manage personal and household finances

Unit 1: Personal budgets

Dylan Busa

Personal budgets

By the end of this unit you will be able to:

  • Draw up an income/expenditure sheet describing plans for projected income and expenditure.
  • Do calculations using computational tools efficiently and correctly and verify solutions in terms of the context.
  • Draw up a personal and/or household budget.
  • Record actual income and expenditure over a period and compare to the projected budget.
  • Identify, discuss and explain variances and methods for financial control.

What you should know

Before you start this unit, make sure you can:

  • Perform basic calculations on a calculator including addition, subtraction, multiplication division and finding percentages.


How to manage money well is one of the fundamental lessons we all need to learn to be successful in life. Very few individuals are born into circumstances where they do not need to manage their money carefully and effectively.

There are a few fundamental but easy to understand principles that you should follow if you want to manage your money and make it work for you.

Principles of managing money

The first and most important of the principles of managing money is this: A part of all you earn is yours to keep. Another way of saying this is that you need to pay yourself first. A good rule of thumb is that you should save at least [latex]\scriptsize 10\%[/latex] of your income. Income is all the money that you earn. Obviously, you can save more than [latex]\scriptsize 10\%[/latex] but [latex]\scriptsize 10\%[/latex] should be the minimum.

But how is this possible, you may ask. I don’t earn enough to save anything. Well, this leads to the second basic principle. Control your expenses. You need to make sure that you don’t spend more than you earn. Expenses are all the things we spend our money on – from food, to clothes, to phones and everything in between. There is a difference between the things we need and the things we want. It can be hard to decide what we really need.

In order to control your expenses, you need to know in detail what they are. This is where a personal budget comes in. A budget is simply a list of all things you expect to spend money on and how much you expect to spend, and all the ways you expect to earn money and what you expect to earn. If the total you expect to spend is more than the total you expect to earn, you have a problem.

Now saving and keeping the money under your bed is not going to do you much good. You need to invest your savings so that your savings can grow, and your money can start to work for you. But it is important that you invest in things you understand, or that you seek the advice of people you trust who are good at investing. We will deal with how money grows through simple and compound interest in the next subject outcome.

Did you know?

Did you know that many of the principles of managing money well were first discovered by people in the ancient city of Babylon over [latex]\scriptsize 3\ 500[/latex] years ago?

Watch the video called “The Richest Man in Babylon – Best Ideas Summary” to learn about the fundamentals of managing money well and growing your wealth.

Take note!

  • Income – this is the money you receive regularly through work or investments.
  • Expenses – this is the money you spend buying goods and services or repaying your debts.
  • Budget – this is a list of all the income you expect to earn and the expenses you expect to have over a given period.

Activity 1.1: Where does my money go?

Time required: 20 minutes

What you need:

  • a pen
  • a piece of paper

What to do:

  1. The first step in making a personal budget is to work out where all your money goes. Make a list of all the things you spent money on last month and how much you spent. Refer back to all your till slips (if you have them) or your bank statement if you used a debit or credit card. If you don’t know what you spent your money on or how much you spent, this is a clear sign that you need to take control of your expenses. Start keeping track. Remember to include expenses like debt repayments and insurance.
  2. Look through your list and divide your expenses into the things you need and the things you want. Be tough! Question every item. Do you really need KFC every week? Do you really need that online music download service?
  3. Work out the total of all your expenses.
  4. Now list all your income and how much each source is. Do you have a job? Do you get a stipend, wage, salary or an allowance? Do friends and family contribute to your expenses? Do you collect a government grant? Calculate the total of all your income.
  5. Work out what [latex]\scriptsize 10\%[/latex] of all your income is and write this down as the amount you should save.
  6. Now calculate what the difference is between what you earn, what you spend and what you should save. If you earn more than you spend and save, well done! You are doing a great job. Why not save even more? If you spend more than you earn, it is time to take a look at those expenses.
  7. Look through all your expenses and decide what a reasonable average monthly amount would be. This is a great opportunity to remove some of your ‘want’ expenses. Your aim is to get your expenses and savings down to less than your income.

What did you find?

Obviously, your income and expenses are completely unique to you. Therefore, we will present an example of what each of the steps above might look like.

  1. Here is a list of typical expenses for various people. Which ones apply to you? Which ones have we left out?
    • Housing
      • Rent or bond repayments
      • Home insurance
      • Electricity
      • Water
      • Property tax
    • Food
      • Groceries and household supplies
      • Take-aways and eating out
      • Other food expenses
    • Transportation
      • Public transportation and taxis
      • Petrol
      • Parking and tolls
      • Car maintenance
      • Car insurance
      • Car loan
      • Other transportation expenses
    • Health
      • Medicines
      • Health insurance
      • Other health expenses
    • Personal and family
      • Childcare
      • Child support
      • Money given or sent to family
      • Clothing and shoes
      • Donations
      • Entertainment
      • Phone and communication
      • Other personal or family expenses
    • Education
      • Tuition
      • Supplies
      • Student loans
    • Financial
      • Bank fees
      • Loan repayments
    • Other expenses
      This is what a list of expenses might look like:
  2. Identify which of your expenses could be categorised as ‘wants’.
  3. Calculate the total of all your expenses.
  4. List your sources of income and your total income.
  5. Show your savings goal based on your current levels of income.
  6. Calculate what money remains at the end of the month. In this example, we can see that more is spent than was earned. In this example, this person needs to cut [latex]\scriptsize \text{R}375[/latex] from their expenses.
  7. In order to spend less money than is earned, the following changes could be made to this budget:
      • change to a cheaper cell phone package
      • cut out all hair products
      • reduce the monthly spend on clothing
      • reduce the monthly spend on take-aways.

    Below is the revised budget. Now there is a surplus of [latex]\scriptsize \text{R445}[/latex] that can be saved for emergencies, saved for something like a car, or invested.

Activity 1.1 showed the basic budgeting process. Now obviously a budget is no good unless you are disciplined and keep to it. You are encouraged to create your own personal budget and to keep to it. Keep track of what you spend each month. If you spend a bit more than you budgeted in one month, you know you need to cut back in the following month(s) to stay on track.

Did you know?

The [latex]\scriptsize 50/30/20[/latex] rule can be an effective guideline with which to create a personal budget.

  • Budget [latex]\scriptsize 50\%[/latex] of your income on things that you need.
  • Budget [latex]\scriptsize 30\%[/latex] of your income on things that you want.
  • Budget [latex]\scriptsize 20\%[/latex] of your income on savings and debt repayments.


If you would like more information on personal budgets and how to create one, visit the following websites:

Example 1.1

Question taken from NC(V) Mathematics L2 Paper 1 February 2013

Kayelani is a painter who works [latex]\scriptsize 21[/latex] days per month. He works for eight hours per day, which is [latex]\scriptsize 168[/latex] hours per month and earns a nett wage of [latex]\scriptsize \text{R}40[/latex] per hour. He works away from home and rents a small flat. His monthly expenses are as follows:

  • Rental of flat (including water and electricity): [latex]\scriptsize \text{R}2\ 150[/latex]
  • Transport: [latex]\scriptsize \text{R16}[/latex] per day
  • Cell phone contract: [latex]\scriptsize \text{R145}[/latex]
  • Groceries: [latex]\scriptsize \text{R1}\ 725.50[/latex]
  • Clothing account: [latex]\scriptsize \text{R450}\text{.50}[/latex]
  • Entertainment: [latex]\scriptsize \text{R500}[/latex]
  • Laundry service: [latex]\scriptsize \text{R}200[/latex]

Use the above information to fill in the income and expenditure sheet below.


We are told that Kayelani works [latex]\scriptsize 168[/latex] hours per month and earns a nett wage of [latex]\scriptsize \text{R}40[/latex] per hour. When we say nett, we mean AFTER all deductions have been made. In other words, he earns [latex]\scriptsize \text{R}40[/latex] per hour after any deductions. If you see the word gross, this means BEFORE any deductions like tax and Unemployment Insurance Fund (UIF).

So Kayelani’s nett wage is [latex]\scriptsize 168\times \text{R}40=\text{R}6\ 720[/latex]. He does not make any additional income, so his nett monthly earnings are also [latex]\scriptsize \text{R}6\ 720[/latex].

Now all his expenses are monthly expenses except transport which is per day. Therefore, to work out his total monthly transport expense, we have to multiply this amount by the number of days he has to travel to work, i.e. [latex]\scriptsize 21[/latex]. His total transport expense is [latex]\scriptsize 21\times \text{R16}=\text{R336}[/latex].

Now we can complete the expenses portion of his income and expenditure sheet.

Here is the final completed sheet.

Exercise 1.1

Sibongile has a personal budget as shown below.

Her income and expenses are as follows for the month of January.


Nett salary: [latex]\scriptsize \text{R}13\ 500[/latex]
Commission: [latex]\scriptsize 10\%[/latex] on sales of [latex]\scriptsize \text{R}28\ 142.40[/latex]


Rent: [latex]\scriptsize \text{R}6\ 000[/latex]
Electricity: [latex]\scriptsize \text{R712}[/latex]
Water: [latex]\scriptsize \text{R490}[/latex]
Car repayment: [latex]\scriptsize \text{R2}\ 767.13[/latex]
Car insurance: [latex]\scriptsize \text{R673}\text{.42}[/latex]
Petrol: [latex]\scriptsize \text{R768}[/latex]
Groceries: [latex]\scriptsize \text{R3}\ 124.87[/latex]
Clothing: [latex]\scriptsize \text{R1}\ \text{813}\text{.23}[/latex]
Cell phone: [latex]\scriptsize \text{R490}\text{.90}[/latex]
Life insurance: [latex]\scriptsize \text{R}600[/latex]
Entertainment: [latex]\scriptsize \text{R874}\text{.45}[/latex]

Answer the following questions.

  1. Complete the income and expenses sheet for the month of January.
  2. Did Sibongile stick to her budget?
  3. In which areas was there a variance between her budget and her actual income and expenditure. In other words, where did she overspend and/or underspend?
  4. What advice could you give to Sibongile to help her save at least [latex]\scriptsize 10\%[/latex] of her income?

The full solutions are at the end of the unit.


In this unit you have learnt the following:

  • The keys to financial success are to spend less than you earn, to save and to invest your savings.
  • How to draw up a projected personal and household monthly budget.
  • How to record actual income and expenditure over a period of time.
  • Identify and explain variances between actual and projected figures.

Unit 1: Assessment

Suggested time to complete: 20 minutes

Question taken from NC(V) Mathematics L2 Paper 1 October 2012

Peter kept a record of all his earnings and all the payments he made during the month of August 2010. Use the information below to complete his income statement (also below).


  • Gross salary: [latex]\scriptsize \text{R}15\ 500[/latex] per month.
  • Deductions from his salary:
    • UIF: [latex]\scriptsize 1\%[/latex] of the gross salary
    • Income tax: [latex]\scriptsize \text{R3}\ 875[/latex]
    • Pension fund: [latex]\scriptsize \text{R110}[/latex]


  • Birthday bonus: [latex]\scriptsize 10\%[/latex] of gross monthly salary
  • Commission: [latex]\scriptsize 7\%[/latex] on his total sales of [latex]\scriptsize \text{R36}\ 490[/latex]


  • House rent: [latex]\scriptsize \text{R4}\ 500.10[/latex]
  • Groceries: [latex]\scriptsize \text{R}1\ 780.15[/latex]
  • Car repayment: [latex]\scriptsize \text{R}1\ 260[/latex]
  • Cell phone: [latex]\scriptsize \text{R275}[/latex]
  • Petrol: [latex]\scriptsize \text{R850}\text{.30}[/latex]
  • Electricity: [latex]\scriptsize \text{R460}[/latex]
  • Water: [latex]\scriptsize \text{R69}\text{.17}[/latex]
  • Clothing accounts: [latex]\scriptsize \text{R}1\ 200[/latex]
  • Insurance: [latex]\scriptsize \text{R218}\text{.19}[/latex]
  • Entertainment: [latex]\scriptsize \text{R480}[/latex]

The full solutions are at the end of the unit.

Unit 1: Solutions

Exercise 1.1

  1. .

  2. Sibongile was not able to stick to her budget.
  3. Sibongile did not earn as much commission as she had budgeted. Her income was, therefore, [latex]\scriptsize \text{R}2\ 185.76[/latex] below budget.
    Sibongile overspent on the following items by the following amounts:
    Electricity: [latex]\scriptsize \text{R62}[/latex]
    Water: [latex]\scriptsize \text{R10}[/latex]
    Groceries: [latex]\scriptsize \text{R124}\text{.87}[/latex]
    Clothing: [latex]\scriptsize \text{R313}\text{.23}[/latex]
    Entertainment: [latex]\scriptsize \text{R24}\text{.75}[/latex]
    Sibongile underspent on the following items by the following amounts:
    Petrol: [latex]\scriptsize \text{R32}[/latex]
    Cell phone: [latex]\scriptsize \text{R9}\text{.10}[/latex]
  4. [latex]\scriptsize 10\%[/latex] of her nett salary is [latex]\scriptsize \text{R}1\ 350[/latex]. Therefore, she needs to cut at least [latex]\scriptsize \text{R}1\ 350-\text{R}1\ 179.45=\text{R170}.55[/latex] from her expenses. The best places to cut would be her clothing and entertainment budgets. Another idea is for Sibongile to cut her overall expenses by [latex]\scriptsize \text{R}2\ 500-\text{R}1\ 350=\text{R}1\ 150[/latex] so that she is not so reliant on making [latex]\scriptsize \text{R}5\ 000[/latex] commission every month. Any additional commission over [latex]\scriptsize \text{R}2\ 500[/latex] would go straight to savings.

Back to Exercise 1.1

Unit 1: Assessment

Deductions from salary:
UIF: [latex]\scriptsize \text{R}15\ 500\times 0.01=\text{R}155[/latex]
Income tax: [latex]\scriptsize \text{R3}\ 875[/latex]
Pension fund: [latex]\scriptsize \text{R110}[/latex]

Salary after deductions (NETT salary):
[latex]\scriptsize \text{R}15\ 500-\text{R}155-\text{R}3\ 875-\text{R}110=\text{R}11\ 360[/latex]

[latex]\scriptsize \text{R}15\ 500\times 0.1=\text{R}1\ 550[/latex]

[latex]\scriptsize \text{R36}\ 490\times 0.07=\text{R2}\ 554.30[/latex]

Back to Unit 1: Assessment

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