Percentages

Question 1

The simple interest on an item worth £40 is 1%.

How much is the interest after 3 years?

Answer 1

40p = 1 %

40p x 3 years = £1.20

Question 2

How do you find the percentage of an amount?

Answer 2

(change/smaller amount ÷ original amount) × 100 = the % the change is of the original amount

Question 3

A car is bought for £7500 and sold for £4500.

What is the percentage depreciation on the car’s value?

Answer 3

7500 - 4500 = 3000

3000 ÷ 7500 = 2/5

2/5 x 100 = 40%

Question 4

Cans of paint are bought for £14 and sold for £17.50.

What is the % profit?

Answer 4

17. 50 - 14.00 = 3.50
18. 50÷14 = 1/4

1/4 x 100 = 25%

Question 5

An item was put on sale for £75. It’s original price was £89.

What % of it’s original price is it being sold at?

Answer 5

75 ÷ 89 = 0.84

0.84 x 100 = 84%

Question 6

For a percentage increase (x%), what do you multiply the number (y) by?

Answer 6

y x 1.x

Question 7

For a percentage decrease (x%), what do you multiply the number (y) by?

Answer 7

100 - x = z

y x 0.z

Question 8

£2000 is in a savings account that earns 1.5% compound interest for 5 years.

£2000 x 1.015ⁿ = the amount in the account after 5 years.

What is n and what does it represent?

Answer 8

5, the amount of years/times the interest is applied

Question 9

£1000 is in a savings account which earns 5% compound interest.
How much will be in the account after 2 years?

Answer 9

£1000 x 1.05² = £1102.50

Question 10

A mountain bike depreciates at 10% each year. It originally cost £650.
How much is it worth after 2 years?

Answer 10

£650 x 0.9² = £526.50

Question 11

(Reverse %)
If an amount is known to be a certain percentage of another amount, how do you work out the original amount?

(E.g. x is 70% of y)

Answer 11

amount ÷ decimal percentage = original amount

x ÷ 0.7 = y

Question 12

140 students attended an event, 30% less than the year before.
How many were there last year?

Answer 12

140 = 70%

140 ÷ 70 = 1% = 2

2 x 100 = 100% = 200 students

OR

140÷0.7 = 200 students

Question 13

With a 10% pay rise, £352 is earnt per week. How much was earnt before the pay rise?

Answer 13

352 = 110%

352÷110 = £3.20 = 1%

£3.20 x 100 = 100% = £320

OR

352÷1.1 = £320

Question 14

What is a percentage?

Answer 14

a proportion that shows a number as parts per hundred

Question 15

What is the difference between simple and compound interest?

Answer 15

Simple interest is always calculated based off the amount not including any interest that is added.

Compound interest is calculated using the amount including any interest that was previously added.