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C1. Ratio & proportion
Repeated proportional change

Vocabulary Two variable are in direct proportion to one another if they are always in the same ratio. If y is proportional to x, we write y µ x. If y=12 when x=3, then y=4x and 4 is refered to as the multiplier. When a value is increased by a percentage, it is often easiest to calculate the change using multipliers. For example a percentage increase of 3% can be found by multiplying the original amount by 1.03 An example £1000 is kept in the bank for 10 years. The rate of interest remains fixed throughout at 5%. Find the amount of money in the bank at the end of 10 years. Solution A rate of 5% is equivalent to a multiplier of 1.05. The amount of money after 10 years is found by calculating: 1000 × 1.0510=£1629 (to the nearest £).

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