PercentagesPercentages

Objectives:B Grade Understand how to calculate successive

percentages

Work out compound interest

Prior knowledge:

Understand :

Finding percentages of quantities – calculator and non calculator

Percentage increase / decrease & percentage multipliers

PercentagesPercentages

Successive increase or decrease questions will have a percentageincrease / decrease that is repeated more than once.Example:

£1000 is put in a bank account that pays 5% interest at the end of each year. Calculate how much there will be after 3 years.

At the end of the first year there will have been a 5% increase

Answer:

The percentage multiplier for a 5% increase is: 1.05

Original quantity × percentage multiplier = new quantity

1000 × 1.05 = 1050At the end of the second year there will have been a 5% increase

1050 × 1.05 = 1102.5At the end of the third year there will have been a 5% increase

1102.5 × 1.05 = 1157.625 £1157.63

PercentagesPercentages

Look at what has been done here

1000 × 1.05

This can be simplified to

The index number represents the number of times the percentage change is repeated

1000 × 1.053

5% of 1000

Look at the difference by calculating one year’s percentage increaseThen multiplying it by 3

1000 × 0.05 = 50

= 1157.625

£1000 + 150 =

( ) × 1.05( ) × 1.05

50 × 3 = 150

1150This is called simple interest because it does not calculate 5% of thenew quantity at the end of the first year