Teach Me Maths

Simple and Compound Interest

Question 12 marks

£600 is invested at 4% simple interest per year. Work out the interest earned in one year, in pounds.

Hint

Interest is a percentage of the original investment.

Worked solution

£600 is invested at 4% simple interest per year. Work out the interest earned in one year, in pounds.

  1. 600\times0.04=24 pounds.

Question 22 marks

£800 is invested at 3% simple interest per year for 5 years. Work out the total interest, in pounds.

Hint

The same interest amount is earned each year.

Worked solution

£800 is invested at 3% simple interest per year for 5 years. Work out the total interest, in pounds.

  1. Annual interest: 800\times0.03=24 pounds.
  2. Total: 24\times5=120 pounds.

Question 32 marks

£1250 is invested at 2% simple interest per year for 4 years. Work out the final balance, in pounds.

Hint

Add the total interest to the original investment.

Worked solution

£1250 is invested at 2% simple interest per year for 4 years. Work out the final balance, in pounds.

  1. Interest: 1250\times0.02\times4=100 pounds.
  2. Balance: 1250+100=1350 pounds.

Question 42 marks

£900 earns 5% simple interest per year. How many years does it take to earn £180 interest?

Hint

Find the interest earned in one year.

Worked solution

£900 earns 5% simple interest per year. How many years does it take to earn £180 interest?

  1. Annual interest: 900\times0.05=45 pounds.
  2. 180\div45=4 years.

Question 53 marks

£1500 earns £180 simple interest over 4 years. Work out the annual percentage interest rate.

Hint

Find one year’s interest as a percentage of the original amount.

Worked solution

£1500 earns £180 simple interest over 4 years. Work out the annual percentage interest rate.

  1. Annual interest: 180\div4=45 pounds.
  2. 45\div1500\times100=3\%.

Question 62 marks

£500 is invested at 10% compound interest per year for 2 years. Work out the final balance, in pounds.

Hint

Each year’s interest is added before the next year.

Worked solution

£500 is invested at 10% compound interest per year for 2 years. Work out the final balance, in pounds.

  1. 500\times1.10=550 pounds after one year.
  2. 550\times1.10=605 pounds after two years.

Question 72 marks

£1000 is invested at 5% compound interest per year. Work out the interest earned during the second year only, in pounds.

Hint

The second year starts with the balance after one year.

Worked solution

£1000 is invested at 5% compound interest per year. Work out the interest earned during the second year only, in pounds.

  1. First-year balance: 1000\times1.05=1050 pounds.
  2. Second-year interest: 1050\times0.05=52.50 pounds.

Question 82 marks

£2000 is invested at 3% compound interest per year for 3 years. Work out the final balance in pounds, to the nearest penny.

Hint

Use the multiplier for all three years; round at the end.

Worked solution

£2000 is invested at 3% compound interest per year for 3 years. Work out the final balance in pounds, to the nearest penny.

  1. A 3% increase makes the balance 103% of its current value, so multiply by 1.03 each year.
  2. After year 1: 2000\times1.03=2060. This becomes the starting balance for year 2.
  3. After year 2: 2060\times1.03=2121.80. This becomes the starting balance for year 3.
  4. After year 3: 2121.80\times1.03=2185.454. There is one factor of 1.03 for each of the 3 years, so this is also 2000\times1.03^3=2185.454.
  5. Round the final balance to the nearest penny: £2185.45.

Question 92 marks

A machine worth £600 loses 20% of its value each year. Work out its value after 2 years, in pounds.

Hint

Each year it keeps 80% of its current value.

Worked solution

A machine worth £600 loses 20% of its value each year. Work out its value after 2 years, in pounds.

  1. A 20% loss leaves 80% of the current value, so multiply by 0.80 each year.
  2. After year 1: 600\times0.80=480. After year 2: 480\times0.80=384.
  3. There is one factor of 0.80 for each of the 2 years, so the same calculation is 600\times0.80^2=384. The machine is worth £384.

Question 101 mark

£1000 is invested at 5% interest per year. Which statement correctly compares simple and compound interest?

Hint

Simple interest always uses the original investment.

Worked solution

£1000 is invested at 5% interest per year. Which statement correctly compares simple and compound interest?

  1. Both earn £50 in every year.
  2. Simple earns £50 each year; compound earns £52.50 in year 2.
  3. Compound earns £50 each year; simple earns £52.50 in year 2.
  4. Both earn £52.50 in year 2.
  1. Simple interest is 1000\times0.05=50 pounds each year.
  2. Compound interest in year 2 is 1050\times0.05=52.50 pounds.

Question 113 marks

£2400 is invested at 2.5% compound interest per year for 3 years. Work out the total interest earned, in pounds to the nearest penny.

Hint

Subtract the original investment from the final balance.

Worked solution

£2400 is invested at 2.5% compound interest per year for 3 years. Work out the total interest earned, in pounds to the nearest penny.

  1. A 2.5% increase makes the balance 102.5% of its current value, so multiply by 1.025 each year.
  2. After year 1: 2400\times1.025=2460. This becomes the starting balance for year 2.
  3. After year 2: 2460\times1.025=2521.50. This becomes the starting balance for year 3.
  4. After year 3: 2521.50\times1.025=2584.5375. One factor is used each year, so the same calculation is 2400\times1.025^3=2584.5375. This is the final balance.
  5. Interest is the amount above the original £2400: 2584.5375-2400=184.5375. Round to the nearest penny: £184.54 interest.

Question 122 marks

A bicycle worth £850 loses 12% of its value each year. Work out its value after 3 years, in pounds to the nearest penny.

Hint

Use 88% of the previous value each year.

Worked solution

A bicycle worth £850 loses 12% of its value each year. Work out its value after 3 years, in pounds to the nearest penny.

  1. A 12% loss leaves 88% of the current value, so multiply by 0.88 each year.
  2. After year 1: 850\times0.88=748. After year 2: 748\times0.88=658.24. After year 3: 658.24\times0.88=579.2512.
  3. There is one factor of 0.88 for each of the 3 years, so the same calculation is 850\times0.88^3=579.2512. To the nearest penny, the bicycle is worth £579.25.

Question 132 marks

£1600 is invested. It earns 4% compound interest in year 1 and 2% in year 2. Work out the final balance, in pounds.

Hint

Use the two different multipliers in order.

Worked solution

£1600 is invested. It earns 4% compound interest in year 1 and 2% in year 2. Work out the final balance, in pounds.

  1. In year 1, 4% interest makes the balance 104% of £1600, so multiply by 1.04: 1600\times1.04=1664. This is the balance starting year 2.
  2. In year 2, 2% interest makes that balance 102% as large, so multiply by 1.02: 1664\times1.02=1697.28.
  3. The rates differ, so use one multiplier for each year in order: 1600\times1.04\times1.02=1697.28. The final balance is £1697.28.

Question 143 marks

An investment earns £210 simple interest in 3 years at 3.5% per year. Work out the original investment, in pounds.

Hint

The total interest is 10.5% of the original.

Worked solution

An investment earns £210 simple interest in 3 years at 3.5% per year. Work out the original investment, in pounds.

  1. 3\times3.5\%=10.5\%.
  2. Original investment: 210\div0.105=2000 pounds.

Question 154 marks

Asha invests £1000 at 4% compound interest per year. Ben invests £1200 at 3% simple interest per year.

After 2 years, how much more interest has Asha earned than Ben? Give your answer in pounds.

Hint

Compare interest earned, not final balances.

Worked solution

Asha invests £1000 at 4% compound interest per year. Ben invests £1200 at 3% simple interest per year.

After 2 years, how much more interest has Asha earned than Ben? Give your answer in pounds.

  1. Asha earns 4% interest on the current balance each year, so each year the balance is multiplied by 1.04 (100\%+4\%=104\%=1.04).
  2. After year 1: 1000\times1.04=1040. This is the new balance and becomes the starting balance for year 2.
  3. After year 2: 1040\times1.04=1081.60. The same calculation is 1000\times1.04^2=1081.60: one factor of 1.04 for each of the 2 years.
  4. Asha’s £1081.60 is her final balance, not her interest. Her interest is 1081.60-1000=81.60, or £81.60.
  5. Ben earns 1200\times0.03=36 pounds each year. Simple interest uses the original £1200 each year, so after 2 years his total interest is 36\times2=72, or £72.
  6. Asha earned 81.60-72=9.60, or £9.60, more interest than Ben.

Question 16Challenge3 marks

A car is bought for £16 000. Its value goes down by 15% in the first year. After that, its value goes down by 10% each year.

Work out the value of the car at the end of 3 years, in pounds.

Hint

The first year uses a different multiplier from the second and third years.

Worked solution

A car is bought for £16 000. Its value goes down by 15% in the first year. After that, its value goes down by 10% each year.

Work out the value of the car at the end of 3 years, in pounds.

  1. End of year 1: 16000\times0.85=13600 pounds.
  2. End of year 2: 13600\times0.90=12240 pounds.
  3. End of year 3: 12240\times0.90=11016 pounds.

Question 17Challenge3 marks

£1000 is invested at 10% compound interest per year. Interest is added at the end of each year.

After how many complete years will the balance first exceed £1300?

Hint

Check successive year-end balances until the threshold is passed.

Worked solution

£1000 is invested at 10% compound interest per year. Interest is added at the end of each year.

After how many complete years will the balance first exceed £1300?

  1. After 1 year: £1100. After 2 years: £1210.
  2. After 3 years: 1210\times1.10=1331 pounds.
  3. £1210 is below £1300; £1331 exceeds it, so 3 years.

Question 18Challenge3 marks

A machine is worth £2000 and loses 20% of its value at the end of each year.

After how many complete years will its value first be less than £1100?

Hint

Check the values year by year, including the year before crossing.

Worked solution

A machine is worth £2000 and loses 20% of its value at the end of each year.

After how many complete years will its value first be less than £1100?

  1. A 20% loss leaves 80% of the current value, or 0.80 of it. Multiply the value by 0.80 each year.
  2. Year 1: 2000\times0.80=1600. Year 2: 1600\times0.80=1280. Both are still above £1100.
  3. Year 3: 1280\times0.80=1024, which is below £1100. The value first falls below £1100 after 3 complete years.

Question 19Challenge4 marks

Both accounts start with £2000. Account A pays 5% compound interest per year. Account B pays 4% compound interest per year.

At the end of year 1, after interest is added, £100 is withdrawn from A. No money is withdrawn from B.

How much more is in B than A at the end of year 2? Give your answer in pounds.

Hint

Apply the withdrawal before A earns its second year’s interest.

Worked solution

Both accounts start with £2000. Account A pays 5% compound interest per year. Account B pays 4% compound interest per year.

At the end of year 1, after interest is added, £100 is withdrawn from A. No money is withdrawn from B.

How much more is in B than A at the end of year 2? Give your answer in pounds.

  1. A after withdrawal: 2000\times1.05-100=2000 pounds.
  2. A after year 2: 2000\times1.05=2100 pounds.
  3. B after year 2: 2000\times1.04^2=2163.20 pounds.
  4. Difference: 2163.20-2100=63.20 pounds.

Question 20Challenge4 marks

£3000 is invested at 2% compound interest per year for 2 years. After the second year’s interest is added, £500 is deposited. The account then earns 3% interest for one more year.

Work out the final balance, in pounds to the nearest penny.

Hint

Keep the deposit separate from the first two years’ interest.

Worked solution

£3000 is invested at 2% compound interest per year for 2 years. After the second year’s interest is added, £500 is deposited. The account then earns 3% interest for one more year.

Work out the final balance, in pounds to the nearest penny.

  1. After 2 years: 3000\times1.02^2=3121.20 pounds.
  2. After deposit: 3121.20+500=3621.20 pounds.
  3. Final balance: 3621.20\times1.03=3729.836 pounds, or £3729.84.

More on this topic: Simple and Compound Interest worksheet with full solutions

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