Question

Percents build on one another in strange ways. It would seem that if you increased a number by 5% and thenincreased its result by 5% more, the overall increase would be 10%.7. Let's do exactly this with the easiest number to handle in percents.(a) Increase 100 by 5%(b) Increase your result form (a) by 5%.(C) What was the overall percent increase of the number 100? Why is it not 10%?

Answer 1

a) 105

b) 110.25

c) Increase of 10.25%. It is not 100% because the second increase of 5% is over the first increased value, not over the initial value.

Explanation:

Increase and multipliers:

Suppose we have a value of a, and want a increse of x%. The multiplier of a increase of x% is given by 1 + (x/100). So the increased value is (1 + (x/100))a.

(a) Increase 100 by 5%

The multiplier is 1 + (5/100) = 1 + 0.05 = 1.05

1.05*100 = 105

(b) Increase your result form (a) by 5%.

1.05*105 = 110.25

(C) What was the overall percent increase of the number 100? Why is it not 10%?

110.25/100 = 1.1025

1.1025 - 1 = 0.1025

Increase of 10.25%. It is not 100% because the second increase of 5% is over the first increased value, not over the initial value.