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Repeated proportional change is when an amount increases or decreases by the same percentage each time, over several time intervals.

For example, the value of a car may decrease each year by the same percentage.

Example

The population of a town increases by 2% every year. It is estimated that at the end of 2025 the population will be 36750.

What will the population be at the end of 2027?

Solution:

At the end of 2026, the population will be 2% more than 36750.

36750 ÷ 100 x 2 = 735
36750 + 735 = 37485

At the end of 2026, the population will be 37485.

At the end of 2027, the population will be 2% more than 37485.

37485 ÷ 100 x 2 = 749.7 (round up to 750)
37485 + 750 = 38235

Answer:

At the end of 2027, the population will be 38235.

Alternative Method

2% = 0.02
1 + 0.02 = 1.02

Multiplying by 1.02 is the same as finding 2% and adding it on – but it is much quicker!

At the end of 2026, the population will be:

36750 x 1.02 = 37485

At the end of 2027, the population will be:

37485 x 1.02 = 38234.7= 38235 (nearest whole number)

Answer:

At the end of 2027, the population will be 38235.