National 5MathsSQARevision NotesNumerical SkillsPercentagesAppreciation & Depreciation

Appreciation & Depreciation (SQA National 5 Maths): Revision Note

Exam code: X847 75

Roger B

Written by: Roger B

Reviewed by: Dan Finlay

Updated on

Working with appreciation

What is appreciation?

  • Appreciation is a type of repeated percentage change

  • It refers to the value of something increasing by percentage amounts over time

    • E.g. the value of a piece of art, a collectible action figure, or an investment account

  • The time period for each change is often a year

    • But changes may also occur monthly, weekly, etc.

    • An exam question will specify what the time period is

  • The rate of percentage increase may be constant, or may vary from period to period

  • Appreciation questions are answered using the usual techniques for repeated percentage change

    • Just be sure to answer in the context of the question

What is compound interest?

  • Compound interest refers to a specific type of appreciation

  • Interest is money that is regularly added to an original amount of money

    • This could be added yearly, monthly, etc.

    • When saving money, interest increases the amount saved

    • With debt, interest increases the amount owed

  • In the exam compound interest questions will usually involve money deposited in a savings or investment account

    • The interest rate will be given as a percentage

      • This is the percentage increase to use when calculating the repeated percentage change

      • E.g. a 4% interest rate will mean to use a percentage multiplier of 1.04 in your calculations

    • The interest period (years, months, etc.) will be specified in the question

  • With compound interest the amount added increases from period to period

    • This is because in the second period interest is earned on the original amount and on the interest added in the first period

    • And in the third period interest is earned on the original amount, the interest added in the first period, and the interest added in the second period

    • Etc.

Examiner Tips and Tricks

Simple interest is a type of interest where the same amount is earned in each period.

  • For example 4% simple interest on a deposit of £100

    • 4% of £100 is £4

    • So a constant £4 is added to the original amount during each period

Questions on simple interest do not normally occur on the National 5 Maths exams.

Worked Example

Callum, an art collector, buys a painting for £425,000 at the end of 2024.

The painting is expected to increase in value by 6% each year.

Calculate the painting's expected value by the end of 2028.

Give your answer correct to the nearest thousand pounds.

Answer:

This is an appreciation question (increasing money value), so it is an example of repeated percentage increase

The percentage multiplier is 1.06 for an increase of 6%

The increases occur four times (4 years from 2024 to 2028)

So multiply 30,000 by 1.06cross times1.06cross times1.06cross times1.06 (or 1.064)

425000 cross times 1.06 to the power of 4 equals 536552.708

Round to the nearest thousand pounds

£537,000 (to nearest £1000)

Worked Example

Màiri invests £1200 in a savings account, which pays compound interest at the rate of 4% per year for 7 years.

To the nearest pound, what is her investment worth at the end of the 7 years?

Answer:

4% compound interest per year means a repeated percentage increase of 4% per year

The multiplier for a 4% increase is 1.04

The increase occurs 7 times (for the seven years)

  • So multiply £1200 by1.04 cross times 1.04 cross times 1.04 cross times 1.04 cross times 1.04 cross times 1.04 cross times 1.04 space equals space 1.04 to the power of 7

1200 cross times 1.04 to the power of 7 equals £ 1579.118135...

Round to the nearest pound

bold £ bold 1579 (to nearest pound)

Working with depreciation

What is depreciation?

  • Depreciation is a type of repeated percentage change

  • It refers to the value of something decreasing by percentage amounts over time

    • E.g. the value of a car, a laptop, or a mobile phone

  • The time period for each change is often a year

    • But changes may also occur monthly, weekly, etc.

    • An exam question will specify what the time period is

  • The rate of percentage decrease may be constant, or may vary from period to period

  • Depreciation questions are answered using the usual techniques for repeated percentage change

    • Just be sure to answer in the context of the question

Worked Example

A car was bought for £30,000.

It depreciated by 12% in the first year.

It then depreciated by a further 8% each year over the next two years.

Calculate the value of the car three years after it was bought.

Answer:

This is a depreciation question, so it is an example of repeated percentage decrease

The percentage multipliers are

  • 0.88 for a decrease of 12%

  • 0.92 for an decrease of 8%

These decreases occur one after the other

  • First a decrease by 12%

  • Then two successive decreases by 8%

So multiply 30,000 by 0.88cross times0.92cross times0.92 (or 0.88cross times0.922)

30000 cross times 0.88 cross times 0.92 squared equals 22344.96

£22,344.96

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    Author
    Reviewer
    Roger B

    Author: Roger B

    Expertise: Maths Content Creator

    Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.

    Dan Finlay

    Reviewer: Dan Finlay

    Expertise: Maths Subject Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.