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Compound interest Quiz

Grade 4 • 4A • 10 Questions (35 Marks)

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Compound interest — Notes & Worked Examples Show / Hide

Explanation:

Compound interest (and depreciation) applies a percentage change to the new balance at the end of each year. Use the multiplier formula: Final Amount = Original × (Multiplier)n, where n is the number of years.

For a compound increase of r%, the multiplier is 1 + r100 (e.g. +3.5% → 1.035). For depreciation (decrease) of r%, the multiplier is 1 − r100 (e.g. −12% → 0.88). Watch out if the question asks for the interest earned only (subtract the original amount at the end).

Example 1: £4000 is invested for 3 years at 2.5% per annum compound interest. Find the total value after 3 years.

Solution:

Multiplier = 100% + 2.5% = 102.5% = 1.025
Amount = 4000 × 1.025³
= 4307.5625 (round to nearest penny)
Answer: £4307.56

Example 2: A car bought for £15,000 depreciates by 18% per year. Work out its value after 4 years (to the nearest £).

Solution:

Multiplier = 100% − 18% = 82% = 0.82
Value = 15,000 × 0.824 = 6781.824
Answer: £6782
Question 1
[1 mark]
£3000 is invested in an account paying 3% compound interest per annum
How much is in the account after 5 years?
£
Worked Solution & Answer
Final Amount = Initial Amount × (1 ± rate100)n
£3477.82
Answer: £ £3477.82
Question 2
[1 mark]
A car is bought for £13,000
It depreciates by 12% each year
What is its value after 3 years?
£
Worked Solution & Answer
Final Amount = Initial Amount × (1 ± rate100)n
£8859.14
Answer: £ £8859.14
Question 3
[3 marks]
Anil wants to invest £25 000 for 3 years in a bank.
Personal BankCompound Interest2% for each yearSecure BankCompound Interest4.3% for the first year0.9% for each extra year
Which bank will give Anil the most interest at the end of 3 years?
You must show all your working.
Worked Solution & Answer
Personal Bank: 25000 × 1.02³ = £26 530.20 (interest = £1530.20) M1
Secure Bank: 25000 × 1.043 × 1.009² = £26 546.46 (interest = £1546.46) M1
Secure Bank gives more interest. A1
Answer: Secure Bank (£26 546.46 vs £26 530.20, or £1546.46 vs £1530.20 interest)
Question Paper (PDF) • Mark Scheme (PDF)
Question 4 OCR Nov 2024 4H Q5
[3 marks]
A person invests £8000 at a rate of 5% per year compound interest.
Calculate the total amount of **interest** earned after 3 years.
£
Worked Solution & Answer
Total value after 3 years = 8000 × 1.05³ = £9261 M2
Total interest earned = 9261 − 8000 = £1261. A1
Answer: £ 1261
Question Paper (PDF) • Mark Scheme (PDF)
Question 5 IGCSE Nov 2021 2F Q23 / 2H Q7
[4 marks]
Ali and Badia each have 25 000 dollars to invest.
Cyclone BankTornado BankInvest 25 000 dollars4.5% compound interest per yearfor 3 yearsInvest 25 000 dollarsReceive 1150 dollars interest each yearfor 3 years
Ali invests in the Cyclone Bank for 3 years.
Badia invests in the Tornado Bank for 3 years.
By the end of the 3 years, Ali will have received more interest than Badia.
How much more?
Show your working clearly.
Give your answer correct to the nearest dollar.
dollars
Worked Solution & Answer
Ali total = 25000 × 1.045³ = $28529.15 ⇒ Ali interest = $3529.15 M2
Badia interest = 3 × 1150 = $3450 M1
Difference = 3529.15 – 3450 = 79.15 = 79 dollars (or 79 or 80) A1
Answer: 79 dollars
Question Paper (PDF) • Mark Scheme (PDF)
Question 6
[4 marks]
Louise invests £x in Better Investments for 3 years.
Sadiq invests £x in County Bank for 3 years.
Better InvestmentsCompound Interest2.5% per annumCounty BankCompound Interest2% per annum for the first two years3.5% per annum for each extra year
At the end of the 3 years, the value of Louise’s investment is £344 605
Work out the value of Sadiq’s investment at the end of the 3 years.
£
Worked Solution & Answer
x = 344 605 ÷ 1.025³ = £320 000 M3
Sadiq: 320 000 × 1.02² × 1.035 = £344 580.48 A1
Answer: £ 344 580.48
Question Paper (PDF) • Mark Scheme (PDF)
Question 7 IGCSE Jan 2023 2F Q23 / 2H Q8
[4 marks]
Matteo is going to invest 5000 Swiss francs for two years.
He can invest his money in Bank G or in Bank H.
Bank G1.6% per yearcompound interestBank H2.9% interest added aftertwo years
The total amount of interest Matteo would receive at the end of two years from Bank G is more than the amount of interest Matteo would receive at the end of two years from Bank H.
How much more?
Swiss francs
Worked Solution & Answer
Bank G: 5000 × 1.016² = 5161.28 ⇒ interest = 161.28 Swiss francs M2
Bank H: 5000 × 0.029 = 145 Swiss francs M1
Difference = 161.28 − 145 = 16.28 Swiss francs. A1
Answer: 16.28 Swiss francs
Question Paper (PDF) • Mark Scheme (PDF)
Question 8 IGCSE Jun 2025 1HR Q11 / 1FR Q26
[5 marks]
Zhou invests some money for 2 years.
He invests $2500 with Bank A and $3000 with Bank B.
Bank AInvests $2500amount of moneyinvested:total amount of interestafter 2 years= 20 : 3Bank BInvests $30004% per year compound interest for 2 years
Zhou receives more **interest** from Bank A than from Bank B.
How much more?
$
Worked Solution & Answer
Bank A interest = (2500 ÷ 20) × 3 = $375 M2
Bank B interest = 3000 × 1.04² − 3000 = $244.80 M2
Difference = 375 − 244.80 = $130.20. A1
Answer: $ 130.20
Question Paper (PDF) • Mark Scheme (PDF)
Question 9 OCR Jun 2024 5H Q12
[5 marks]
(a) Sasha invests £1000 at a rate of 5% per year compound interest.
Sasha says:
"After one year, my investment will get £50 in interest and will be worth £1050.
Therefore, after two years, my investment will get another £50 in interest and will be worth £1100."
Is Sasha correct?
Give a reason for your answer.
(b) Sasha buys a car.
The value, £V, of the car after n years is given by the formula
V = a × bn.
The graph shows some information about the value of the car.
(a) Sasha invests £1000 at a rate of 5% per year compound interest.
Sasha says:
"After one year, my investment will get £50 in interest and will be worth £1050.
Therefore, after two years, my investment will get another £50 in interest and will be worth £1100."
Is Sasha correct?
Give a reason for your answer. [1 mark]
(b) Sasha buys a car.
The value, £V, of the car after n years is given by the formula
V = a × bn.
The graph shows some information about the value of the car. [4 marks]
800064001VnNot to scale
Find the value of a and the value of b.
Worked Solution & Answer
(a)
Compound interest is calculated on the new amount (£1050) in year 2, not the original £1000. C1
Answer (a): No, because in the second year the 5% interest is calculated on £1050 (giving £52.50 interest, total £1102.50).
(b)
When n = 0, V = 8000 ⇒ a = 8000 M3
When n = 1, V = 6400 ⇒ 8000 × b = 6400 ⇒ b = 6400 ÷ 8000 = 0.8. A1
Answer (b): a = 8000, b = 0.8
Question Paper (PDF) • Mark Scheme (PDF)
Question 10 Specimen Set 1 3H Q8
[5 marks]
Ian invested an amount of money at 3% per annum compound interest.
At the end of 2 years the value of the investment was £2652.25
(a) Work out the amount of money Ian invested. [3 marks]
£
(b) [2 marks]
Saver Account4% per annumcompound interest.Investment Account21% interest paid at theend of 5 years.
Worked Solution & Answer
(a)
2652.25 ÷ 1.03² = 2652.25 ÷ 1.0609 = £2500 M2 A1
Answer (a): £ 2500
(b)
1.04⁵ = 1.21665... → 21.67% > 21%, so Saver Account is best M1 A1
Answer (b): Saver Account (gives 21.67% interest, which is greater than 21%)
Question Paper (PDF) • Mark Scheme (PDF)
Score: 0 / 10 (0 / 35 marks)
Compound interest Worksheets Next: Indices (index laws) →

Grade 4 Quizzes

24 Topics
4A - Compound interest4B - Indices (index laws)
4C - Prime factors HCF and LCM4D - Real life graphs
4E - Inequalities on a number line4F - Solving inequalities
4G - Forming and solving equations4H - nth term of a linear sequence
4J - Expanding and factorising4K - Pythagoras theorem
4L - Angles in parallel lines4M - Angles in polygons
4N - Surface area4P - Volume of a cuboid
4Q - Volume of a prism4R - Bearings
4S - Cylinders4T - Plans and elevations
4U - Scatter graphs4V - Probability
4W - Averages from tables4X - Reverse mean
4Y - Area of a trapezium4Z - Loci and construction