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ScotlandApplications of MathematicsSyllabus dot point

How do interest rates affect savings and borrowing, and how do you compare simple interest, compound interest, hire purchase and loans?

Investigating the impact of interest rates on savings and borrowing, calculating simple and compound interest, finding appreciation and depreciation, and comparing the total cost of borrowing through loans and hire purchase.

A focused answer to the SQA National 5 Applications of Mathematics finance content on savings and borrowing, covering the impact of interest rates, calculating simple and compound interest, appreciation and depreciation using a multiplier, and comparing the total cost of borrowing through loans and hire purchase.

Generated by Claude Opus 4.812 min answer

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  1. What this dot point is asking
  2. Simple and compound interest
  3. Appreciation and depreciation
  4. Loans and hire purchase
  5. Examples in context
  6. Try this

What this dot point is asking

The SQA wants you to investigate how interest rates affect savings and borrowing: calculate simple and compound interest, find appreciation and depreciation using a multiplier, and compare the total cost of borrowing through a loan or hire purchase.

Simple and compound interest

Interest is the cost of borrowing money or the reward for saving it. There are two kinds, and they behave very differently over time.

Higher interest rates grow savings faster but also make borrowing more expensive, which is the impact the SQA asks you to investigate.

Appreciation and depreciation

Appreciation is a rise in value over time (such as a house); depreciation is a fall (such as a car). Both use a multiplier raised to a power, exactly like compound interest.

The only difference from compound interest is the direction: depreciation uses a multiplier below 11, appreciation a multiplier above 11.

Loans and hire purchase

Borrowing to buy something usually costs more than paying cash. Hire purchase spreads the cost over a deposit plus regular instalments, and a loan charges interest on the amount borrowed.

Examples in context

These calculations drive real money decisions. A saver compares two accounts by their compound interest; a buyer weighs paying cash against hire purchase for a car or sofa; an owner estimates a car's resale value after depreciation. Each rests on choosing simple or compound interest correctly, using a multiplier for appreciation or depreciation, and totalling the full cost of borrowing, the skills here.

Try this

Q1. Find the simple interest on £600\pounds 600 at 4%4\% for 22 years. [2 marks]

  • Cue. 600×0.04×2=£48600 \times 0.04 \times 2 = \pounds 48.

Q2. £1000\pounds 1000 earns 2%2\% compound interest for 33 years. Find the total. [3 marks]

  • Cue. 1000×1.023=£1061.211000 \times 1.02^3 = \pounds 1061.21.

Q3. Hire purchase is a deposit of £80\pounds 80 plus 1212 payments of £20\pounds 20. Find the total cost. [2 marks]

  • Cue. 80+12×20=£32080 + 12 \times 20 = \pounds 320.

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 N5 Apps style3 marksMaria invests £2500\pounds 2500 in an account paying 3%3\% compound interest per year. Calculate the value of her investment after 22 years.
Show worked answer →

Compound interest multiplies by the same factor each year. A 3%3\% rise multiplies by 1.031.03 (1 mark). Over 22 years the value is 2500×1.0322500 \times 1.03^2 (1 mark). Evaluate: 1.032=1.06091.03^2 = 1.0609, so 2500×1.0609=£2652.252500 \times 1.0609 = \pounds 2652.25 (1 mark). Markers reward the multiplier 1.031.03, raising it to the power 22, and the rounded value. Compound interest earns interest on previous interest, unlike simple interest.

SQA N5 Apps style4 marksA sofa costs £800\pounds 800 cash, or on hire purchase a deposit of £150\pounds 150 plus 2424 monthly payments of £32\pounds 32. How much more does hire purchase cost than paying cash?
Show worked answer →

Find the total of the monthly payments: 24×£32=£76824 \times \pounds 32 = \pounds 768 (1 mark). Add the deposit for the total hire purchase cost: £150+£768=£918\pounds 150 + \pounds 768 = \pounds 918 (1 mark). Compare with the cash price: £918−£800=£118\pounds 918 - \pounds 800 = \pounds 118 (1 mark). State the extra cost clearly: hire purchase costs £118\pounds 118 more (1 mark). Markers reward the total payments, the total HP cost including the deposit, and the difference. Forgetting the deposit is a frequent error.

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