Repeated Percentage Change - Worksheets, Questions and Revision

21 original exam-style questions - 8 pages of questions with a full mark scheme - free printable PDF.

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6.4 Repeated Percentage Change

EDEXCEL 1MA1 · Calculator allowed · about 95 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Ravi buys a motorbike for £3200. It depreciates (loses value) by 12% in its first year.
(a)Write down the multiplier used to decrease an amount by 12%.(1)
(b)Work out the value of the motorbike after 1 year.(2)
(Total for Question 1 is 3 marks)
2
Which of these is the correct single decimal multiplier for an increase of 4.5%?
  • A) 0.45
  • B) 1.45
  • C) 1.045
  • D) 0.955
(Total for Question 2 is 1 mark)
3
A mobile phone contract costs £45 per month. The price increases by 6% each year.
(a)Write down the multiplier for an increase of 6%.(1)
(b)Write down the multiplier for a decrease of 32%.(1)
(c)Work out the cost per month of the phone contract after 2 years. Give your answer to the nearest penny.(2)
(Total for Question 3 is 4 marks)
4
Amara invests £1500 in a savings account that pays 3% per annum compound interest. She leaves the money in the account for 2 years and makes no withdrawals.

Work out the value of Amara's investment at the end of the 2 years. Give your answer to the nearest penny.
(Total for Question 4 is 3 marks)
5
A delivery company buys a new van for £18000.
The van depreciates by 20% in its first year and then by 15% in its second year.
(a)Work out the value of the van after 2 years.(3)
(b)Work out the total depreciation over the 2 years as a percentage of the original £18000.(2)
(Total for Question 5 is 5 marks)
6
Ben invests £2400 in an account paying 2.5% per annum compound interest. He makes no further deposits or withdrawals.
(a)Show that the value of Ben's investment after 2 years is £2521.50(2)
(b)Work out the value of Ben's investment after 5 years. Give your answer to the nearest penny.(3)
(Total for Question 6 is 5 marks)
7
A laptop depreciates in value by 18% each year. After 3 years, the laptop is worth £468.66.

Work out the value of the laptop when it was new. Give your answer to the nearest pound.
(Total for Question 7 is 3 marks)
8
A tractor was bought for £45000. It depreciates by 12% per year for the first 2 years, then by 8% per year after that.
(a)Show that the value of the tractor after 2 years is £34848(3)
(b)Work out the value of the tractor after a total of 4 years. Give your answer to the nearest pound.(3)
(Total for Question 8 is 6 marks)
9
Grace's salary was £28000. It increased by 4% in year 1, by 3% in year 2, and by 2.5% in year 3.
(a)Work out Grace's salary after year 3. Give your answer to the nearest penny.(3)
(b)Work out the overall percentage increase in Grace's salary over the three years. Give your answer correct to 1 decimal place.(2)
(Total for Question 9 is 5 marks)
10
The price of a laptop is £750 now. Due to inflation, the price increases by 2% each year.

Work out the price of the laptop in 4 years' time. Give your answer to the nearest penny.
(Total for Question 10 is 3 marks)
11
Farida has an unpaid credit card balance of £850. The credit card company charges 22% per annum compound interest on any unpaid balance, applied at the end of each year. Farida makes no payments.
(a)Work out the amount Farida owes after 2 years. Give your answer to the nearest penny.(3)
(b)Work out the total interest charged over the 2 years.(2)
(Total for Question 11 is 5 marks)
12
A jacket in a shop costs £80.
In a spring sale, the price is reduced by 25%.
After the sale, the price is then increased by 20%.
The jacket is then reduced by a further 10% in a winter sale.
(a)Work out the price of the jacket after all three changes.(3)
(b)Work out the overall percentage change in the price of the jacket compared with the original £80. State whether this is an increase or a decrease.(2)
(Total for Question 12 is 5 marks)
13
A house was bought for £210000. In year 1 its value increased by 4%. In year 2, due to a market correction, its value decreased by 1.5%. In year 3 its value increased by 3%.
(a)Calculate the value of the house at the end of year 3. Give your answer to the nearest pound.(4)
(b)Calculate the overall percentage change in the value of the house over the 3 years. Give your answer correct to 1 decimal place.(2)
(Total for Question 13 is 6 marks)
14
Chidi invests £5000 for 4 years. He compares two accounts.
Bank A: 2% per annum compound interest.
Bank B: simple interest at 2.2% per annum, calculated on the original £5000 only, each year.

Determine which bank gives the higher return after 4 years, and by how much.
(Total for Question 14 is 5 marks)
15
The population of a village is 2400. The population increases by 3% each year.

Work out the number of complete years it takes for the population to first exceed 3000. Show your working.
(Total for Question 15 is 3 marks)
16
A car is valued at £9000. Its value depreciates by 15% each year. An insurance company writes off the car once its value falls below £4000.

Determine, with working, whether the car has been written off after 5 years.
(Total for Question 16 is 4 marks)
17
Priya invests £600. She says: 'If I increase my investment by 10% and then decrease the new amount by 10%, I will end up back at £600.'

Show that Priya is wrong, and find the actual final amount.
(Total for Question 17 is 3 marks)
18
Two towns have populations that grow each year.
Town A: population 12000, grows by 5% per year.
Town B: population 15000, grows by 2% per year.

Determine, with working, whether Town A's population will exceed Town B's population within 10 years. If so, state after how many complete years this first happens.
(Total for Question 18 is 5 marks)
19
A car was bought for £24000. After 3 years it is worth £14739. The car depreciates by the same percentage each year.

Work out the annual rate of depreciation.
(Total for Question 19 is 4 marks)
20
Sam invested a sum of money in an account that pays 3.5% per annum compound interest. She makes no further deposits or withdrawals. After 6 years, the investment is worth £2458.51.

Work out how much Sam originally invested. Give your answer to the nearest penny.
(Total for Question 20 is 4 marks)
21
A quantity increases by r% each year, compounded annually, for n years.
(a)Write down a formula for the value V of an investment of £P after n years, growing at r% per annum compound interest.(2)
(b)Use your formula to find the value of £3200 invested for 7 years at 1.8% per annum compound interest. Give your answer to the nearest penny.(3)
(Total for Question 21 is 5 marks)
Mark scheme · 6.4 Repeated Percentage Change

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21