Transcript percentages successive percentages

Percentages
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
Percentages
Successive increase or decrease questions will have a percentage
increase / 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.
Answer:
At the end of the first year there will have been a 5% increase
The percentage multiplier for a 5% increase is: 1.05
Original quantity × percentage multiplier = new quantity
1000 × 1.05 = 1050
At the end of the second year there will have been a 5% increase
1050 × 1.05 = 1102.5
At the end of the third year there will have been a 5% increase
1102.5 × 1.05 = 1157.625
£1157.63
Percentages
Look at what has been done here
((1000 × 1.05) × 1.05) × 1.05 = 1157.625
This can be simplified to
1000 × 1.053
The index number represents the number of times the percentage
change is repeated
Look at the difference by calculating one year’s percentage increase
Then multiplying it by 3
5% of 1000
1000 × 0.05 = 50
50 × 3 = 150
£1000 + 150 = 1150
This is called simple interest because it does not calculate 5% of the
new quantity at the end of the first year