Ever wondered how your savings grow over time or why... Show more
Maths87 views·Updated Jun 1, 2026·2 pagesUnderstanding Discrete Growth and Decay
Scarlett Edwardes@scarlett_1917
1
of 2
Understanding Growth and Decay
Think of compound interest as money that earns money on itself - it's like a snowball effect that keeps building up. This concept works for anything that changes value over time, from your savings account earning interest to your laptop depreciating in value.
When something appreciates (increases in value), you add the interest rate to 1. For example, 4% interest becomes 1.04 as a multiplier. When something depreciates (loses value), you subtract from 1 - so 10% depreciation becomes 0.9.
Let's see this in action: Claire has £1000 earning 4% annual interest. After converting 4% to 1.04, we calculate 1.04⁵ = 1.217, then multiply by £1000 to get £1217 after 5 years.
Quick Tip: Always convert percentages to decimals first, then add to 1 for growth or subtract from 1 for decay!
2
of 2
Working with Depreciation and Reverse Problems
Depreciation follows the same pattern but in reverse - Joe's £2000 car losing 10% annually becomes 0.9² = 0.81, giving us £2000 × 0.81 = £1620 after 2 years.
Sometimes you'll face reverse percentage problems where you know the final amount but need the original. If a shirt costs £15 after a 70% discount, you know £15 represents 30% of the original price .
To find the original price, work out what 10% equals: £15 ÷ 3 = £5 . Then multiply by 10 to get 100%: £5 × 10 = £50 original price.
Exam Strategy: For reverse problems, always identify what percentage your given amount represents first!
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Maths87 views·Updated Jun 1, 2026·2 pagesUnderstanding Discrete Growth and Decay
Scarlett Edwardes@scarlett_1917
Ever wondered how your savings grow over time or why your phone loses value so quickly? Discrete growth and decayexplains exactly how amounts change through compound interest - whether that's money growing in your bank account or your car... Show more
1
of 2Sign up to see the content. It's free!
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Understanding Growth and Decay
Think of compound interest as money that earns money on itself - it's like a snowball effect that keeps building up. This concept works for anything that changes value over time, from your savings account earning interest to your laptop depreciating in value.
When something appreciates (increases in value), you add the interest rate to 1. For example, 4% interest becomes 1.04 as a multiplier. When something depreciates (loses value), you subtract from 1 - so 10% depreciation becomes 0.9.
Let's see this in action: Claire has £1000 earning 4% annual interest. After converting 4% to 1.04, we calculate 1.04⁵ = 1.217, then multiply by £1000 to get £1217 after 5 years.
Quick Tip: Always convert percentages to decimals first, then add to 1 for growth or subtract from 1 for decay!
2
of 2Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Working with Depreciation and Reverse Problems
Depreciation follows the same pattern but in reverse - Joe's £2000 car losing 10% annually becomes 0.9² = 0.81, giving us £2000 × 0.81 = £1620 after 2 years.
Sometimes you'll face reverse percentage problems where you know the final amount but need the original. If a shirt costs £15 after a 70% discount, you know £15 represents 30% of the original price .
To find the original price, work out what 10% equals: £15 ÷ 3 = £5 . Then multiply by 10 to get 100%: £5 × 10 = £50 original price.
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