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5 Jan 2026

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2 pages

Understanding Discrete Growth and Decay

Scarlett Edwardes

@scarlett_1917

Ever wondered how your savings grow over time or why... Show more

DISCRETE GROWTH AND DECAY
DESCRIPTION:
THIS RELATES TO HOW AN AMOUNT FLUCTUATES UNDER COMPOUND INTEREST.
THIS CAN BE BOTH POSITIVE AND NEGAT

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!

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 $since 100% - 70% = 30%$ .

To find the original price, work out what 10% equals: £15 ÷ 3 = £5 $since 30% ÷ 3 = 10%$ . 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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Maths

•

5 Jan 2026

•

2 pages

Understanding 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

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Understanding Growth and Decay

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!

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Improve your grades

Join milions of students

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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.

To find the original price, work out what 10% equals: £15 ÷ 3 = £5 $since 30% ÷ 3 = 10%$ . 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!