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Topic 08 · 14 lessons

Money & Finance

Money maths is probably the maths you will use most often as an adult. Savings accounts, loans, credit cards, mortgages, pay slips and household bills all involve percentages, rates and a little algebra.

These lessons explain how interest really works, why compound growth is so powerful and how to build a budget that adds up. They are educational, not financial advice.

Lessons in this topic

  1. 8.1Recognising and Counting MoneyEvery coin and note has a value. To count a handful of money, start with the biggest and add the rest in order of size.
  2. 8.2Adding Prices and Finding ChangeLine up pounds and pence when you add prices. Find change by counting on from the price to the amount you paid.
  3. 8.3Multiplying Prices and Sharing BillsMultiply the price of one item by how many you buy. To share a bill equally, divide the total by the number of people.
  4. 8.4Budgeting with MathsA budget is a plan that makes sure money in is at least money out, and maths keeps it honest.
  5. 8.5Saving Towards a GoalTo reach a goal, work out how much is left to save, then divide by the amount you save each time.
  6. 8.6Comparing Prices and Unit CostsUnit cost is the price of one unit. Divide the price by the amount to compare packs of different sizes.
  7. 8.7Discounts and Sale PricesA discount takes a percentage off the price. Find the amount off and subtract it, or multiply by what you still pay.
  8. 8.8Percentage Increase and DecreaseTo increase by p% multiply by 1 + p/100. To decrease multiply by 1 - p/100. Percentage change is the change divided by the original.
  9. 8.9Profit and LossProfit is selling price minus cost price when that is positive. If it is negative there is a loss. Percentage profit compares profit with the cost.
  10. 8.10Tax on a Price: A Worked Percentage ExampleA sales tax adds a percentage to the price. Multiply by 1.2 to add 20%, and divide by 1.2 to go back.
  11. 8.11Currency Conversion with a Given RateAn exchange rate tells you how much of one currency equals one unit of another. Multiply to go one way and divide to go back.
  12. 8.12Interest and PercentagesInterest is the price of money: a percentage paid for borrowing it, or earned for lending it.
  13. 8.13Compound InterestWith compound interest, each period earns interest on everything so far, including past interest. Growth snowballs.
  14. 8.14Borrowing: Principal, Interest and Total RepaymentWhen you borrow, you repay the principal plus interest. Total repayment minus the amount borrowed is the cost of borrowing.

The big ideas

a)Percentages everywhere
Interest rates, tax, discounts and price rises are all percentages, so working fluently with percentages is the core skill.
b)Interest on interest
With compound interest, each period earns interest on the previous interest, so growth speeds up over time.
c)Time is a multiplier
Small regular amounts, given long enough, can grow far beyond what simple addition would suggest.
d)In ≥ out
A budget is just an inequality: spending must not exceed income. Tracking both sides honestly is what makes it work.

Worked example

Saving for a bike

You save $450 in an account paying 4%4\% simple interest per year. How much interest do you earn in 33 years?

  1. Simple interest: I=P×r×tI = P \times r \times t.
  2. Write the rate as a decimal: 4%=0.044\% = 0.04.
  3. Calculate: I=450×0.04×3=54I = 450 \times 0.04 \times 3 = 54.

Answer: You earn $54 interest, for a total of $504.

Where you will meet it

Comparing savings accounts, understanding the true cost of a loan, planning for a holiday and checking a pay slip all use the ideas in this section.

The wider field

Money & Finance also covers these ideas, which build on the lessons above:

  • Profit and loss
  • Tax and VAT
  • Exchange rates
  • Loans and APR
  • Inflation
  • Unit pricing