Budgeting with Maths

What you will learn

• Build a monthly budget from income and expenses.
• Use percentage guidelines such as 50/30/20.
• Check whether a budget balances.

Before you start: you should be able to add and subtract money and find percentages. See Adding Prices and Finding Change and Multiplying Prices and Sharing Bills.

The idea

A budget is a plan for your money. It lists what comes in (income) and what goes out (expenses) over a set period, usually a month. The goal is simple:

$\text{income} - \text{expenses} \geq 0$

If the result is positive, you have a surplus to save. If it is negative, you have a deficit, and you are spending money you don’t have.

Fixed and variable costs

• Fixed costs stay the same each month: rent, subscriptions, a phone contract.
• Variable costs change: food, transport, entertainment.

Fixed costs are predictable; variable costs are where most budgeting decisions happen.

Percentage guidelines

A popular starting point is the 50/30/20 split: about $50\%$ of take-home income on needs, $30\%$ on wants and $20\%$ on savings or paying off debt. It is a guideline, not a law, but it turns a vague intention into numbers you can check.

Worked examples

Example 1: Building a monthly budget

Sam takes home £1,850 a month. Expenses: rent £720, bills £140, food £260, transport £95, phone £18, entertainment £150, clothing £60. Is there a surplus?

1. Total expenses: $720 + 140 + 260 + 95 + 18 + 150 + 60 = 1443$.
2. Balance: $1850 - 1443 = 407$.
3. As a percentage of income: $407 \div 1850 \times 100\% \approx 22\%$.

Answer: a surplus of £407 a month, about $22\%$ of income.

Example 2: Applying 50/30/20

What would a 50/30/20 split look like on Sam’s £1,850?

1. Needs: $0.5 \times 1850 = 925$.
2. Wants: $0.3 \times 1850 = 555$.
3. Savings: $0.2 \times 1850 = 370$.
4. Sam’s needs (rent, bills, food, transport, phone) total £1,233, which is $\approx 67\%$, above the guideline. Housing costs are often the reason.

Answer: £925 / £555 / £370; Sam’s needs are higher, so savings come from cutting wants.

Example 3: A savings goal

Priya wants £1,200 for a laptop in $8$ months. She already has £320. How much must she save each month?

1. Amount still needed: $1200 - 320 = 880$.
2. Divide by months: $880 \div 8 = 110$.

Answer: £110 per month.

Example 4: Unit pricing

Cereal costs £2.40 for 500 g or £3.90 for 750 g. Which is better value?

1. Price per 100 g, small box: $2.40 \div 5 = £0.48$.
2. Price per 100 g, large box: $3.90 \div 7.5 = £0.52$.

Answer: the smaller box is cheaper per gram, so bigger is not always better value.

Small regular costs add up: £3.20 a day on coffee is $3.20 \times 365 = £1,168$ a year. Annualising daily spending is an eye-opening budgeting trick.

Why it matters

Budgeting is probably the most useful everyday application of maths. It relies on addition, percentages, ratios, division and estimation, all skills from earlier lessons, applied to decisions that affect real life: avoiding debt, saving for something important, and coping with unexpected bills. Even young children can practise by planning how to spend pocket money.

This lesson is educational and is not financial advice.