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Ratio, proportion and rates of changeFoundation and Higher

Interest, growth and decay GCSE questions with answers

8 interest, growth and decay questions to try, each with the answer and the full working one tap away. Every question here was made and worked out by the Show Working maths engine, not typed in by hand.

This topic covers simple interest, compound interest, depreciation, and how many years it takes an amount to grow or fall past a value. Compound changes use a multiplier, such as 1.04 for a 4% increase each year.

Quiz yourself: 8 questions

Worked example 1: simple interest

Amir puts £2,400 into a savings account. The account pays 3% simple interest per year. How much interest will Amir get in 2 years?

  1. Interest for one year: 3% of £2,400 = £2,400 × 3 ÷ 100 = £72.00.
  2. Simple interest is the same every year, so for 2 years: 2 × £72.00 = £144.00.

Answer £144.00

01 / Quiz yourselfTry it, then tap to check

Interest, growth and decay questions to try

Work each one out on paper first. Then open the answer and compare your working with ours, step by step.

01 / Simple interestBoth tiers

Chloe borrows £2,500. Simple interest is charged at 6% per year. Chloe pays everything back at the end of 8 years. How much does Chloe pay back altogether?

Show the answer and working
  1. Interest for one year: 6% of £2,500 = £2,500 × 6 ÷ 100 = £150.00.
  2. Simple interest is the same every year, so for 8 years: 8 × £150.00 = £1,200.00.
  3. Add it to the amount borrowed: £2,500 + £1,200.00 = £3,700.00.

Answer £3,700.00

02 / Simple interestBoth tiers

Beth puts £3,800 into a savings account. The account pays 3% simple interest per year. How much interest will Beth get in 7 years?

Show the answer and working
  1. Interest for one year: 3% of £3,800 = £3,800 × 3 ÷ 100 = £114.00.
  2. Simple interest is the same every year, so for 7 years: 7 × £114.00 = £798.00.

Answer £798.00

03 / Simple interestBoth tiers

Isla puts £4,150 into a savings account. The account pays 2.5% simple interest per year. How much will be in the account after 10 years?

Show the answer and working
  1. Interest for one year: 2.5% of £4,150 = £4,150 × 2.5 ÷ 100 = £103.75.
  2. Simple interest is the same every year, so for 10 years: 10 × £103.75 = £1,037.50.
  3. Add it to the amount put in: £4,150 + £1,037.50 = £5,187.50.

Answer £5,187.50

04 / Compound interest and depreciationBoth tiers

Maya invests £10,200 in a savings account. The account pays 1.8% compound interest per year. Work out how much is in the account after 4 years. Give your answer to the nearest penny.

You can use a calculator for this one.

Show the answer and working
  1. The amount in the account goes up by 1.8% each year, so the multiplier is 100% + 1.8% = 101.8% = 1.018.
  2. After 4 years: £10,200 × 1.0184 = £10,954.4678…
  3. To the nearest penny: £10,954.47.

Answer £10,954.47

05 / Compound interest and depreciationBoth tiers

Beth invests £14,700 in a savings account. The account pays 3.5% compound interest per year. Work out how much is in the account after 8 years. Give your answer to the nearest penny.

You can use a calculator for this one.

Show the answer and working
  1. The amount in the account goes up by 3.5% each year, so the multiplier is 100% + 3.5% = 103.5% = 1.035.
  2. After 8 years: £14,700 × 1.0358 = £19,357.0928…
  3. To the nearest penny: £19,357.09.

Answer £19,357.09

06 / Compound interest and depreciationBoth tiers

Grace invests £4,500 in a savings account. The account pays 4.2% compound interest per year. Work out how much interest Grace earns in 3 years. Give your answer to the nearest penny.

You can use a calculator for this one.

Show the answer and working
  1. The amount in the account goes up by 4.2% each year, so the multiplier is 100% + 4.2% = 104.2% = 1.042.
  2. After 3 years: £4,500 × 1.0423 = £5,091.1473…
  3. Interest = £5,091.1473… − £4,500 = £591.1473…
  4. To the nearest penny: £591.15.

Answer £591.15

07 / Growth and decay: how many years?Both tiers

A scientist puts 700 bacteria in a dish. The number of bacteria grows by 15% every hour. After how many whole hours will there first be more than 2,000 bacteria?

You can use a calculator for this one.

Show the answer and working
  1. The amount goes up by 15% each hour, so the multiplier is 100% + 15% = 115% = 1.15.
  2. Multiply by 1.15 once for each hour. The ANS key on your calculator makes this quick. The values (shown to the nearest whole number) are 805 after 1 hour, 926 after 2 hours, 1,065 after 3 hours, 1,224 after 4 hours, 1,408 after 5 hours, 1,619 after 6 hours, 1,862 after 7 hours, 2,141 after 8 hours.
  3. After 7 hours it is 1,862, which is not yet more than 2,000.
  4. After 8 hours it is 2,141, which is more than 2,000. So the answer is 8 hours.

Answer 8 hours

08 / Growth and decay: how many years?Both tiers

A house is worth £230,000. Its value goes up by 5% each year. After how many years will the house first be worth more than £300,000?

You can use a calculator for this one.

Show the answer and working
  1. The amount goes up by 5% each year, so the multiplier is 100% + 5% = 105% = 1.05.
  2. Multiply by 1.05 once for each year. The ANS key on your calculator makes this quick. The values are £241,500.00 after 1 year, £253,575.00 after 2 years, £266,253.75 after 3 years, £279,566.44 after 4 years, £293,544.76 after 5 years, £308,222.00 after 6 years.
  3. After 5 years it is £293,544.76, which is not yet more than £300,000.
  4. After 6 years it is £308,222.00, which is more than £300,000. So the answer is 6 years.

Answer 6 years

02 / What's covered3 kinds of question

Interest, growth and decay at GCSE and where marks go

  • Simple interestBoth tiers
  • Compound interest and depreciationBoth tiers
  • Growth and decay: how many years?Both tiers

Worked example 2: growth and decay: how many years?

A patient is given 200 mg of a medicine. Each hour, the amount of the medicine in their body goes down by 30%. After how many whole hours will there first be less than 80 mg in their body?

You can use a calculator for this one.

  1. The amount goes down by 30% each hour, so the multiplier is 100% − 30% = 70% = 0.7.
  2. Multiply by 0.7 once for each hour. The ANS key on your calculator makes this quick. The values (shown to 1 decimal place) are 140 mg after 1 hour, 98 mg after 2 hours, 68.6 mg after 3 hours.
  3. After 2 hours it is 98 mg, which is not yet less than 80 mg.
  4. After 3 hours it is 68.6 mg, which is less than 80 mg. So the answer is 3 hours.

Answer 3 hours

A common mistake

Using simple interest when the question says compound. £500 at 4% compound interest for 3 years is £500 × 1.04³ = £562.43 to the nearest penny, not £500 + 3 × £20 = £560.

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