Percentages » Growth factors

See also Calculating faster with percentages.

Contents:

1. Growth factors with increase
2. Growth factors with decrease

1. Growth factors with increase

An increase of 7% is the same result as multiplying with 1.07.
We call 1.07 a growth factor.

In other words:
With an increase of 7% you will get 107%.
The growth factor that corresponds with 107% = 107 : 100 = 1.07.

Written as a formula it look like this:

With an increase of p% the growth factor is
g = 100 + p100  or shorter: g = 1 + p100.

Vice versa, the growth factor g gives a percentage increase of p = 100(g – 1).

Example 1

Stan earns € 820.
He gets a 2.5% raise for three consecutive years.

Every year is salary will be multiplied with a growth factor 1 + 2.5100 = 1.025, so after three years he will earn 820 × 1.0253 = € 883.05.

Example 2

Margot earns € 935.
After getting a p% raise for two consecutive years, she earns € 1030.84.

935 × g2 = 1030.84 
g2 = 1030.84935
g = square root(1030.84/935 = 1.05

Thus p = 100(1.05 – 1) = 5%.

Example 3

A growing plant increases its height every week with 20%.
How many per cent is the increase per day?

To answer this question, we have to do the following three steps:
1) Calculate the growth factor per week.
2) Then calculate the growth factor per day.
3) Finally, calculate the percentage per day.

Answer:
1) The growth factor per week is 1 + 20100 = 1.2.
2) The growth factor per day is seventh root(1.2) ≈ 1.026.
3) The increase per day is (1.026 – 1) × 100 = 2.6%.

2. Growth factors with decrease

A decrease of 7% gives the same result as multiplying with 0.93.
We call 0.93 in that case also a growth factor.
Because the growth factor is between 0 and 1, you have a decrease.

The rules are:

With a decrease of p% the growth factor is
g = 100 – p100  or shorter: g = 1 – p100.

Vice versa, the growth factor g gives a percentage decrease of p = 100(1 – g).

Example 1

A pair of pants of € 80 is reduced by 24%, what will be the new price?

The growth factor is g = 1 – 24100 = 0.76.
The pair of pants will cost 80 × 0.76 = 60.80 euros.

Example 2

A jacket of € 120 is reduced in price to € 105, what percentage was the price reduction?

The growth factor has been g = 105 : 120 = 0.875.
The percentage decrease is therefore 100(1 – 0,875) = 12.5%.


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