Compound Interest and Depreciation - Worksheets, Questions and Revision

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GCSE · Ratio, Proportion and Rates of Change

4.1 Compound Interest and Depreciation

EDEXCEL 1MA1 · Calculator allowed · about 85 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Which multiplier would be used to increase an amount by 12%?

A) 0.12
B) 1.12
C) 1.2
D) 12.12

(Total for Question 1 is 1 mark)

Which multiplier would be used to decrease an amount by 8%?

A) 1.08
B) 0.92
C) 0.8
D) 0.08

(Total for Question 2 is 1 mark)

Amelia puts 600 pounds into a savings account that pays simple interest at a rate of 2% per year. Calculate the total amount in the account after 3 years.

(Total for Question 3 is 2 marks)

Ben invests 750 pounds in an account that pays compound interest at a rate of 4% per year. Work out the value of his investment after 1 year.

(Total for Question 4 is 2 marks)

Sam invests 300 pounds in an account that pays compound interest at a rate of 6% per year.

(a)Sam invests 300 pounds in an account that pays compound interest at a rate of 6% per year. Write down the multiplier, as a decimal, that represents a 6% increase.(1)

(b)Use your multiplier to work out the value of Sam's investment after 2 years.(2)

(Total for Question 5 is 3 marks)

Chloe invests 1200 pounds in a savings account that pays compound interest at a rate of 3% per year. Calculate the value of her investment after 2 years. Give your answer to the nearest penny.

(Total for Question 6 is 3 marks)

A car is bought for 9000 pounds. It depreciates in value by 15% per year. Work out the value of the car after 2 years.

(Total for Question 7 is 3 marks)

Show that investing 800 pounds at a compound interest rate of 5% per year gives a value of 882 pounds after 2 years.

(Total for Question 8 is 3 marks)

Bilal invests 950 pounds in an account that pays compound interest at a rate of 2% per year. Calculate the value of his investment after 4 years. Give your answer to the nearest penny.

(Total for Question 9 is 3 marks)

Priya invests 2500 pounds in a savings account that pays compound interest at a rate of 2.5% per year. Calculate the total interest she earns after 3 years. Give your answer to the nearest penny.

(Total for Question 10 is 4 marks)

Priti invests 500 pounds for 3 years. She compares two different types of account.

(a)Priti invests 500 pounds in an account that pays simple interest at a rate of 4% per year. Calculate the total amount in the account after 3 years.(2)

(b)Priti's friend invests 500 pounds in a different account that pays compound interest at a rate of 4% per year. Calculate the total amount in this account after 3 years. Give your answer to the nearest penny.(3)

(c)State which account gives the greater return, and work out by how much.(1)

(Total for Question 11 is 6 marks)

A car is bought new for 18000 pounds. It depreciates by 25% in its first year and by a further 12% in its second year. Work out the value of the car after 2 years.

(Total for Question 12 is 4 marks)

Nia is investing 500 pounds at a compound interest rate of 6% per year for 3 years.

(a)To find the value of 500 pounds invested at a compound interest rate of 6% per year for 3 years, Nia calculated 500 x 0.06 x 3 = 90, and gave the total value as 590 pounds. Identify the error in Nia's method.(1)

(b)Work out the correct total value of the investment after 3 years. Give your answer to the nearest penny.(3)

(Total for Question 13 is 4 marks)

A laptop depreciates in value by 20% during its first year of use. After one year it is worth 640 pounds. Work out the original price of the laptop.

(Total for Question 14 is 3 marks)

Tom invests 3000 pounds in an account that pays compound interest at a rate of 3% per year. Use trial and improvement to find the number of complete years after which his investment first exceeds 3500 pounds.

(Total for Question 15 is 3 marks)

Deepa and her brother each invest 2000 pounds for 5 years, in different types of account.

(a)Account A pays compound interest at a rate of 2.5% per year. Deepa invests 2000 pounds in Account A. Calculate the total amount in Account A after 5 years. Give your answer to the nearest penny.(3)

(b)Account B pays simple interest at a rate of 3% per year. Deepa's brother invests 2000 pounds in Account B. Calculate the total amount in Account B after 5 years.(2)

(c)State which account gives the greater return after 5 years, and work out by how much.(2)

(Total for Question 16 is 7 marks)

A vintage guitar increases in value (appreciates) by 4% per year. Marcus bought the guitar for 1200 pounds. Work out its value after 3 years. Give your answer to the nearest penny.

(Total for Question 17 is 3 marks)

A machine was bought for 5000 pounds. After 2 years it is worth 4050 pounds. The machine depreciated by the same percentage each year. Work out the annual rate of depreciation.

(Total for Question 18 is 3 marks)

A van depreciates by 20% in its first year and by a further 15% in its second year. After 2 years the van is worth 5100 pounds. Work out the original value of the van.

(Total for Question 19 is 3 marks)

Fatima invests 4000 pounds in an account that pays compound interest at a rate of 3% per year for the first 2 years. After 2 years the interest rate changes to 5% per year for the third year. Work out the value of her investment after 3 years. Give your answer to the nearest penny.

(Total for Question 20 is 4 marks)

An investment of 2000 pounds grows to 2282.33 pounds after 3 years of compound interest. Use trial and improvement to find the annual rate of interest, correct to 1 decimal place.

(Total for Question 21 is 4 marks)

Mark scheme · 4.1 Compound Interest and Depreciation

Question 1

B1 B identified, 1.12
Answer: B) 1.12

Question 2

B1 B identified, 0.92
Answer: B) 0.92

Question 3

M1 600 x 0.02 x 3 (= 36), or 1 year's interest (12) found and multiplied by 3
A1 636 (pounds) cao
Answer: 636 pounds

Question 4

M1 750 x 1.04, or 750 x 0.04 (= 30) found
A1 780 (pounds) cao
Answer: 780 pounds

Question 5

(a) B1 1.06
(a) Answer: 1.06
(b) M1 300 x 1.06² (= 300 x 1.1236), ft their multiplier from (a)
(b) A1 337.08 (pounds) cao
(b) Answer: 337.08 pounds

Question 6

M1 1.03² (= 1.0609), or 1.03 x 1.03
M1 1200 x their 1.0609
A1 1273.08 (pounds) cao
Answer: 1273.08 pounds

Question 7

M1 0.85² (= 0.7225), or 0.85 x 0.85
M1 9000 x their 0.7225
A1 6502.50 (pounds) cao
Answer: 6502.50 pounds

Question 8

M1 1.05² (= 1.1025), or 1.05 x 1.05
M1 800 x their 1.1025 (dependent on correct multiplier)
A1 882 cso (answer given, full working shown)
Answer: 882 pounds (as given)

Question 9

M1 1.02⁴ (= 1.08243216), or repeated multiplication by 1.02
M1 950 x their 1.08243216
A1 1028.31 (pounds) cao
Answer: 1028.31 pounds

Question 10

M1 1.025³ (= 1.076890625)
M1 2500 x their 1.076890625 (= 2692.2265625, the total value)
M1 their total value - 2500 (method to find interest only)
A1 192.23 (pounds) cao
Answer: 192.23 pounds

Question 11

(a) M1 500 x 0.04 x 3 (= 60)
(a) A1 560 (pounds) cao
(a) Answer: 560 pounds
(b) M1 1.04³ (= 1.124864)
(b) M1 500 x their 1.124864
(b) A1 562.43 (pounds) cao
(b) Answer: 562.43 pounds
(c) B1 compound account, by 2.43 (pounds) ft from (a) and (b)
(c) Answer: The compound interest account, by 2.43 pounds

Question 12

M1 18000 x 0.75
A1 13500 (pounds), the value after year 1
M1 their 13500 x 0.88
A1 11880 (pounds) cao
Answer: 11880 pounds

Question 13

(a) B1 correctly identifies that Nia has used the simple interest method (multiplying by 0.06 x 3), instead of compounding the interest each year on the growing balance
(a) Answer: Nia used simple interest instead of compound interest
(b) M1 1.06³ (= 1.191016)
(b) M1 500 x their 1.191016
(b) A1 595.51 (pounds) cao
(b) Answer: 595.51 pounds

Question 14

M1 identifies multiplier 0.8 (100% - 20%)
M1 640 / 0.8
A1 800 (pounds) cao
Answer: 800 pounds

Question 15

M1 trial at n = 5: 3000 x 1.03⁵ = 3477.82 (too low)
M1 trial at n = 6: 3000 x 1.03⁶ = 3582.15 (exceeds 3500)
A1 6 (years) cao
Answer: 6 years

Question 16

(a) M1 1.025⁵ (= 1.131408212890625)
(a) M1 2000 x their 1.131408212890625
(a) A1 2262.82 (pounds) cao
(a) Answer: 2262.82 pounds
(b) M1 2000 x 0.03 x 5 (= 300)
(b) A1 2300 (pounds) cao
(b) Answer: 2300 pounds
(c) B1 Account B ft from (a) and (b)
(c) B1 37.18 (pounds) ft, correct difference
(c) Answer: Account B, by 37.18 pounds

Question 17

M1 1.04³ (= 1.124864)
M1 1200 x their 1.124864
A1 1349.84 (pounds) cao
Answer: 1349.84 pounds

Question 18

M1 4050 / 5000 (= 0.81)
M1 √0.81 (= 0.9), to find the annual multiplier
A1 10% cao
Answer: 10%

Question 19

M1 0.8 x 0.85 (= 0.68), combined multiplier for 2 years
M1 5100 / their 0.68
A1 7500 (pounds) cao
Answer: 7500 pounds

Question 20

M1 1.03² (= 1.0609)
M1 their 1.0609 x 1.05 (= 1.113945)
M1 4000 x their 1.113945
A1 4455.78 (pounds) cao
Answer: 4455.78 pounds

Question 21

M1 trial at 4%: 2000 x 1.04³ = 2249.73 (too low)
M1 trial at 5%: 2000 x 1.05³ = 2315.25 (too high)
M1 trial at 4.5%: 2000 x 1.045³ = 2282.33 (matches)
A1 4.5% cao
Answer: 4.5%

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Compound Interest and Depreciation - Worksheets, Questions and Revision

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4.1 Compound Interest and Depreciation

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Question 21

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