Transcript Percentages and Interest - School

GCSE
Mathematics
Targeting Grade C
Number
Unit 4 Percentages
and Interest
Can you:
If not you need
TOP: Review how to find simple
percentages
•Find percentages of amounts
Practice 1: Splitting percentages
up
•Find percentage increase or decrease
Practice 2: Finding percentage
increase and decrease
Try a test
TAIL 1
•Find simple interest
Practice 3: Finding simple interest
•Find compound interest
Practice 4: Finding compound
interest
Try a test
TAIL 2
TOP: Solve these simple percentage questions.
(1)
Find 10% of £20
(2)
Find 50% of £100
(3)
Find 30% of £60
(4)
Find 70% of £120
(5)
Find 75% of £200
Lesson
Remember to split the
amount into 10% (by dividing
by 10) and then multiply by
the number of 10s you need!
Practice 1:
Solve these percentage problems.
(1)
Find 35% of £120
(2)
Find 83% of £250
(3)
Find 12% of 75kg
Split your percentage into parts
like 10%, 5%, 2 ½% and 1%
Remember to find 10%, then
1% (by dividing your 10% by 10),
(4)
(5)
Find 17 ½% of 70 miles
Find 24% of £65.50
Lesson
or 5% (by dividing your 10% by 2),
or ½% (by dividing your 1% by 2),
or 2 ½% (by dividing 5% by 2.
Practice 2:
(1)
Find these percentage increases.
Increase £100 by 15%
(2)
Increase 85kg by 12 ½%
(3)
Increase 754 m by 68%
Find these percentage decreases.
(4)
Decrease £100 by 75%
(5)
Decrease 65 miles by 34%
(6)
Decrease 378 km by 7 ½%
Lesson
One way to increase or
decrease amounts by
percentages is to find the
percentage and then add (to
increase) or subtract (to
decrease)
TAIL 1
Are you ready for
the answers ?
(1) The selling price of a computer is the list price
plus VAT at 17 ½ %. The list price of a
(1) 17 ½ /100  786 = 137.55
computer is £786.
Work out the selling price of the computer.
(2) Work out 60% of 5300 kg.
137.55 + 786 = £923.55
(2) 60/100  5300 = £3180
(3) Frances sees three different advertisements for jeans.
Bob’s – 15% off £30
Disco’s – ⅔ of £36
Sanjay’s – £22 + 17 ½% VAT
Work out the cost of the jeans in each advertisement.
(3) (a) 15/100  30 = £4.50
(a)
Bob's
(b)
(c)
Disco's
Sanjay's
30 – 4.50 = 25.50
(b) 2/3  36 = £24
(c) 17.5/100  22 + 22 = £25.80
Lesson
Practice 3:
Find the simple interest for the following:
(1)
£60 for 2 years at 4% interest per annum
(2)
£150 for 3 years at 7.5% interest per annum
(3)
£5000 for 6 years at 3% p.a.
(4)
£2500 for 10 years at 12.5% p.a.
(5)
£750 for 5 years at 6.5% p.a.
Lesson
Find the interest for
one year then
multiply by the
number of years!
Practice 4:
(1)
Find the compound interest for the following:
£150 for 2 years at 7% p.a.
(2)
£500 for 3 years at 12% p.a.
(3)
£7500 for 3 years at 3.5% p.a.
(4)
£65 for 2 years at 5% p.a.
(5)
£2500 for 4 years at 6.5% p.a.
Lesson
Remember the formula
(1+(percentage  100))number of years
to help you e.g. for (1) do
£150  (1.07)2
TAIL 2
(1)
Yesterday Simon repaired a computer and
(1) 5/100  269.30 = 13.465
charged a total of £269.30. Simon reduces his
charges by 5% when he is paid promptly. He
269.30 – 13.465 =
was paid promptly for yesterday's work on the
computer.
255.835 = £255.84
Work out how much he was paid.
(2)
Jane is going to buy a computer for £480 + 17 ½ (2) 17 ½ /100  480 + 480
% VAT. Work out the total price, including VAT,
that Jane will pay for the computer.
= 84 + 480 = £564
(3)
Find the simple interest on £2500 invested for 2
(3) 6/100  2500 = 150
years at 6% per year.
“150”  2 = £300
(4)
£5000 is invested for 3 years at 4% per annum
compound interest. Work out the total interest
earned over the three years.
(4) 1.043  5000 = £5624.32
(5)
Work out the simple interest on £530 at 4.5% per(5) 4.5/100  530 = 23.85
annum after 3 years.
Lesson
Are you ready for
the answers ?
“23.85”  3 = £71.55