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ScotlandApplications of MathematicsSyllabus dot point

How do tax, inflation and insurance affect personal financial planning and the real value of money?

Applying personal financial planning skills, including income tax and national insurance, the effect of inflation on purchasing power, and analysing insurance premiums, excess and risk.

A focused answer to the SQA Higher Applications of Mathematics finance content on personal financial planning, covering income tax and national insurance, inflation and purchasing power, and insurance premiums, excess and risk.

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  1. What this dot point is asking
  2. Income tax and national insurance
  3. Inflation and purchasing power
  4. Insurance, premiums, excess and risk
  5. Try this

What this dot point is asking

The SQA wants you to apply personal financial planning: calculate income tax and national insurance, understand how inflation erodes purchasing power, and analyse insurance through premiums, excess and risk. These skills turn the time-value tools of the area into practical decisions about earning, spending and protecting money.

Income tax and national insurance

Income tax is charged on earnings above a tax-free allowance (the personal allowance). Income above the allowance is taxed, often in bands: a basic rate up to a threshold, then higher rates on income above it.

Inflation and purchasing power

Inflation is the general rise in prices over time. It means a fixed amount of money buys less in the future, even though the number of pounds is unchanged.

So a savings account must pay more than the inflation rate just to keep its real value. If inflation is 4%4\% and an account pays 3%3\%, the money grows in pounds but shrinks in what it can buy. This is the same compound model as growth, used to judge real value.

Insurance, premiums, excess and risk

Insurance lets a person trade a small certain cost for protection against a large uncertain loss. You pay a premium (regularly or annually); if you make a valid claim, the insurer pays out, but you usually pay an excess (the first part of any claim) yourself.

Try this

Q1. Someone earns £25 000\pounds 25\,000 with a £12 570\pounds 12\,570 tax-free allowance and a 20%20\% rate above it. Find the income tax. [2 marks]

  • Cue. Taxable =25000−12570=12430= 25000 - 12570 = 12430; tax =12430×0.20=£2486= 12430 \times 0.20 = \pounds 2486.

Q2. A £500\pounds 500 item rises with inflation of 5%5\% a year. Find its price in 22 years. [2 marks]

  • Cue. 500×1.052=500×1.1025=£551.25500 \times 1.05^{2} = 500 \times 1.1025 = \pounds 551.25.

Q3. Explain why a higher insurance excess usually comes with a lower premium. [2 marks]

  • Cue. With a higher excess the policyholder pays more of each claim, so the insurer's expected payout is lower, allowing a lower premium.

Exam-style practice questions

Practice questions written in the style of SQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

SQA Higher Apps style5 marksA worker earns £32 000\pounds 32\,000 a year. The first £12 570\pounds 12\,570 is tax-free, and income above this is taxed at 20%20\%. Find the income tax due and the take-home pay, ignoring other deductions.
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The taxable amount is the income above the tax-free allowance: 32000−12570=£19 43032000 - 12570 = \pounds 19\,430 (2 marks).

Tax at 20%20\% on this is 19430×0.20=£388619430 \times 0.20 = \pounds 3886 (2 marks).

Take-home pay is 32000−3886=£28 11432000 - 3886 = \pounds 28\,114 (1 mark). Markers reward subtracting the allowance before taxing, applying the rate only to the taxable portion, and the final net figure.

SQA Higher Apps style4 marksA basket of goods costs £200\pounds 200. If inflation runs at 4%4\% a year, find the expected cost in 33 years, and explain what happens to the purchasing power of £200\pounds 200 held in cash over that time.
Show worked answer →

The cost grows by 4%4\% a year, so after 33 years it is 200×1.043=200×1.1249=£224.97200 \times 1.04^{3} = 200 \times 1.1249 = \pounds 224.97 (2 marks).

The same £200\pounds 200 in cash still buys goods worth £200\pounds 200 at today's prices, but those goods now cost about £225\pounds 225, so the cash buys less (1 mark).

Purchasing power has fallen: £200\pounds 200 now buys only about 2001.1249=£177.79\dfrac{200}{1.1249} = \pounds 177.79 worth of today's goods in three years' time (1 mark). Markers reward growing the price by the inflation multiplier and explaining that cash loses real value as prices rise.

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