Compound-Interest Aqa Foundation

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Exam code:8300

Compound interest

What is compound interest?

Compound interest is where interest is calculated on the running total, not just the starting amount
- This is different from simple interest where interest is only based on the starting amount
e.g. £ 100 earns 10% interest each year, for 3 years
- At the end of year 1, 10% of £ 100 is earned
  - The total balance will now be 100+10 = £ 110
- At the end of year 2, 10% of £ 110 is earned
  - The balance will now be 110+11 = £ 121
- At the end of year 3, 10% of £ 121 is earned
  - The balance will now be 121+12.1 = £ 133.10

How do I calculate compound interest?

Compound interest increases an amount by a percentage, and then increases the new amount by the same percentage
- This process repeats each time period (yearly or monthly etc)
We can use a multiplier to carry out the percentage increase multiple times
- To increase £ 300 by 5% once, we would find 300×1.05
- To increase £ 300 by 5%, each year for 2 years, we would find (300×1.05)×1.05
  - This could be rewritten as 300×1.05²
- To increase £ 300 by 5%, each year for 3 years, we would find ((300×1.05)×1.05)×1.05
  - This could be rewritten as 300×1.05³
This can be extended to any number of periods that the interest is applied for
- If £ 2000 is subject to 4% compound interest each year for 12 years
- Find 2000×1.04¹², which is £ 3202.06
Note that this method calculates the total balance at the end of the period, not the interest earned

How do I calculate depreciation?

A similar method can be used if something decreases in value by a percentage every year (e.g. a car)
This is known as depreciation
Change the multiplier to one which represents a percentage decrease
- e.g. a decrease of 15% would be a multiplier of 0.85
If a car worth £ 16 000 depreciates by 15% each year for 6 years
- Its value will be 16 000 × 0.85⁶, which is £ 6034.39

Compound interest formula

An alternative method is to use the following formula to calculate the final balance
- Final balance = $P open parentheses 1 plus r over 100 close parentheses to the power of n space end exponent$ where
  - P is the original amount,
  - r is the % increase,
  - and n is the number of years
- Note that $1 plus r over 100$ is the same value as the multiplier
  - e.g. 1.15 for 15% interest
This formula is not given in the exam

Examiner Tips and Tricks

Double check if the question uses simple interest or compound interest
The formula for compound interest is not given in the exam

Worked Example

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

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

We want an increase of 4% per year, this is equivalent to a multiplier of 1.04, or 104% of the original amount

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