MODULE 4MODULE 4Business-related Business-related

MathematicsMathematics

Chapter 20Principles of Financial Mathematics

20.1 Percentage Change20.1 Percentage Change

A percentage increase or decrease is the amount of the increase or decrease expressed as a percentage of the original value.

Percentage change = amount of change X 100

original value 1

Calculating the amount of the Calculating the amount of the discount and the new pricediscount and the new price

Discount = Reduction in original price/value

If an r% discount is applied, then:

discount = r x original price 100 1

New price = original price – discount = (100 – r) x original price

100 1 Refer to Example 1 page 524

Calculating the amount of the Calculating the amount of the increase and the new priceincrease and the new price

Mark Up = Increase in original price/value

If an r% increase is applied, then:

increase = r x original price 100 1

New price = original price + increase = (100 + r) x original price

100 1Refer to Example 2 page 524

Calculating the amount of the Calculating the amount of the increase and the new priceincrease and the new price

Mark Up = Increase in original price/value

If an r% increase is applied, then:

increase = r x original price 100 1

New price = original price + increase = (100 + r) x original price

100 1Refer to Example 2 page 524

Percentage discount = discount x 100 original price 1

or

Percentage increase = increase x 100 original price 1

Refer to Example 3 page 525

Calculating the original priceCalculating the original price

Sometimes we are given the new price and the percentage increase or decrease (r %), and asked to determine the original price.

This can be done by rearranging the formulas for the new price to make the original price the subject.

When an r% discount has been applied:

Original price = new price x 100 1 ( 100 – r )

When an r% increase has been applied:

Original price = new price x 100 1 ( 100 + r )

Refer to Example 4 page 526