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Interest & Depreciation (Edexcel IGCSE Maths)
Revision Note
Compound Interest
What is compound interest?
- Compound interest is where interest is paid on the interest from the previous year (or whatever time frame is being used), as well as on the original amount
- This is different from simple interest where interest is only paid on the original amount
- Simple interest goes up by the same amount each time whereas compound interest goes up by an increasing amount each time
How do you work with compound interest?
- Keep multiplying by the decimal equivalent of the percentage you want (the multiplier, p)
- A 25% increase (p = 1 + 0.25) each year for 3 years is the same as multiplying by 1.25 × 1.25 × 1.25
- Using powers, this is the same as × 1.253
- In general, the multiplier p applied n times gives an overall multiplier of pn
- If the percentages change varies from year to year, multiply by each one in order
- a 5% increase one year followed by a 45% increase the next year is 1.05 × 1.45
- In general, the multiplier p1 followed by the multiplier p2 followed by the multiplier p3... etc gives an overall multiplier of p1p2p3...
Compound interest formula
- Alternative method: A formula for the final ("after") amount is where...
- ...P is the original ("before") amount, r is the % increase, and n is the number of years
- Note that is the same value as the multiplier
Examiner Tip
- It is easier to multiply by the decimal equivalent "raised to a power" than to multiply by the decimal equivalent several times in a row
Worked example
Jasmina invests £1200 in a savings account which pays compound interest at the rate of 2% per year for 7 years.
To the nearest pound, what is her investment worth at the end of the 7 years?
We want an increase of 2% per year, this is equivalent to a multiplier of 1.02, or 102% of the original amount
This multiplier is applied 7 times;
Therefore the final value after 7 years will be
Round to the nearest pound
Alternative method
Or use the formula for the final amount
Substitute P is 1200, r = 2 and n = 7 into the formula
£1378 (to the nearest pound)
Depreciation
What is meant by depreciation?
- Depreciation is where an item loses value over time
- For example: cars, game consoles, etc
- Depreciation is usually calculated as a percentage decrease at the end of each year
- This works the same as compound interest, but with a percentage decrease
How do I calculate a depreciation?
- You would calculate the new value after depreciation using the same method as compound interest
- Identify the multiplier, p (1 - "% as a decimal")
- 10% depreciation would have a multiplier of p = 1 - 0.1 = 0.9
- 1% depreciation would have a multiplier of p = 1 - 0.01 = 0.99
- Raise the multiplier to the power of the number of years (or months etc)
- Multiply by the starting value
- Identify the multiplier, p (1 - "% as a decimal")
- New value is
- A is the starting value
- p is the multiplier for the depreciation
- n is the number of years
- Alternative method: A formula for the final ("after") amount is where...
- ...P is the original ("before") amount, r is the % decrease, and n is the number of years
- If you are asked to find the amount the value has depreciated by:
- Find the difference between the starting value and the new value
Worked example
Mercy buys a car for £20 000. Each year its value depreciates by 15%.
Find the value of the car after 3 full years.
Identify the multiplier
100% - 15% = 85%
p = 1 - 0.15 = 0.85
Raise to the power of number of years
0.853
Multiply by the starting value
£20 000 × 0.853
= £12 282.50
Alternative method
Or use the formula for the final amount
Substitute P is 20 000, r = 15 and n = 3 into the formula
£12 282.50
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