GCSE Simple and compound interest Practice Questions

Free GCSE Simple and compound interest practice questions with full step-by-step worked solutions. Covers simple interest, percentage of an amount, one year, I = PRT/100. Practise exam-style problems and check your method.

simple interestpercentage of an amountone yearI = PRT/100total amountcompound interest
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
Ravi invests £2000\pounds 2000 in an account paying 5%5\% simple interest per year. Work out the interest he earns in 11 year.
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Worked solution

  1. Write down the simple interest formula

    I=P×R×T100I = \frac{P \times R \times T}{100}

    Simple interest is worked out on the ORIGINAL amount every year, so one formula covers all the years.

  2. Substitute the values

    I=2000×5×1100I = \frac{2000 \times 5 \times 1}{100}

    P = £2000 is the amount invested, R=5R = 5 is the rate and T=1T = 1 is the number of years.

  3. Work out the interest

    I=10000100=£100I = \frac{10000}{100} = \pounds 100

    The interest earned is £100.

Answer
£100\pounds 100
Question 2
2 markseasy
Amira invests £500\pounds 500 at 4%4\% compound interest per year. Which calculation works out the value of her investment after 33 years?
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Worked solution

  1. Find the multiplier for one year

    100%+4%=104%=1.04100\% + 4\% = 104\% = 1.04

    One year of 4% compound interest multiplies the balance by 1.04.

  2. Apply the multiplier once for each year

    500×1.04×1.04×1.04500 \times 1.04 \times 1.04 \times 1.04

    Each year the WHOLE balance (including interest already earned) is multiplied by 1.04.

  3. Write the repeated multiplication as a power

    500×1.043500 \times 1.04^{3}

    Multiplying by 1.04 three times is 1.04 cubed. Note that 500 x 1.04 x 3 would be wrong: that is simple interest, not compound.

Answer
500×1.043500 \times 1.04^{3}
Question 3
2 marksintermediate
A tractor costs £16 000\pounds 16\,000. Its value depreciates by 30%30\% each year. Which calculation gives the value of the tractor after 22 years?
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Worked solution

  1. Find the multiplier for one year

    100%−30%=70%=0.7100\% - 30\% = 70\% = 0.7

    Losing 30% leaves 70% of the value, so the multiplier is 0.7.

  2. Apply the multiplier once for each year

    16000×0.7×0.716000 \times 0.7 \times 0.7

    The second year 30% is taken off the NEW value, not off the original £16 000.

  3. Write it as a power

    16000×0.7216000 \times 0.7^{2}

    Two years of the same multiplier is 0.7 squared.

  4. Work out the value

    16000×0.49=£784016000 \times 0.49 = \pounds 7840

    The tractor is worth £7840 after 2 years.

  5. Reject the common wrong method

    16000×0.4=£640016000 \times 0.4 = \pounds 6400

    Taking off 60% in one go (30% + 30%) gives £6400, which is too small. The 30% in year 2 is a smaller amount of money than the 30% in year 1.

  6. State the correct calculation

    16000×0.72=£784016000 \times 0.7^{2} = \pounds 7840

    The correct calculation is 16 000 x 0.7 squared.

Answer
16000×0.72=£784016000 \times 0.7^{2} = \pounds 7840
Question 4
4 markshard
Leah puts £1000\pounds 1000 into an account paying 5%5\% compound interest per year. At the end of each year, immediately after the interest has been added, she pays in a further £200\pounds 200. Work out how much is in the account at the end of 33 years.
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Worked solution

  1. Plan the year-by-year table

    balance→balance×1.05→(+ deposit)\text{balance} \to \text{balance} \times 1.05 \to (+\, \text{deposit})

    Each year: add the interest first (multiply by the multiplier), then add the extra payment. The next year's interest is earned on the bigger balance. Exam convention: keep the full unrounded balance in the calculator all the way through and round to the nearest penny only at the very end.

  2. Write the yearly percentage as a multiplier

    100%+5%=105%=1.05100\% + 5\% = 105\% = 1.05

    A 5% increase keeps the whole 100% and adds 5% on top, so multiply by 1.05 each year.

  3. Year 1: add the interest

    £1000×1.05=£1050\pounds 1000 \times 1.05 = \pounds 1050

    Interest of £50.00 is added to £1000, giving £1050.

  4. Year 1: add the extra payment

    £1050+£200=£1250\pounds 1050 + \pounds 200 = \pounds 1250

    The £200 payment goes in AFTER the interest, so it earns no interest until next year. Balance: £1250.

  5. Year 2: add the interest

    £1250×1.05=£1312.50\pounds 1250 \times 1.05 = \pounds 1312.50

    Interest of £62.50 is added to £1250, giving £1312.50.

  6. Year 2: add the extra payment

    £1312.50+£200=£1512.50\pounds 1312.50 + \pounds 200 = \pounds 1512.50

    The £200 payment goes in AFTER the interest, so it earns no interest until next year. Balance: £1512.50.

  7. Year 3: add the interest

    £1512.50×1.05≈£1588.13\pounds 1512.50 \times 1.05 \approx \pounds 1588.13

    Interest of £75.63 is added to £1512.50, giving £1588.13.

  8. Year 3: add the extra payment

    £1588.13+£200≈£1788.13\pounds 1588.13 + \pounds 200 \approx \pounds 1788.13

    The £200 payment goes in AFTER the interest, so it earns no interest until next year. Balance: £1788.13.

  9. Round to the nearest penny

    £1788.13→£1788.13\pounds 1788.13 \to \pounds 1788.13

    Every line above kept the exact balance; round once, here.

  10. State the answer

    £1788.13\pounds 1788.13

    After 3 years the account holds £1788.13.

Answer
£1788.13\pounds 1788.13
Question 5
6 markschallenging
Jonah opens an account with £500\pounds 500. The account pays 6%6\% compound interest per year. At the end of each year, immediately after the interest has been added, Jonah pays in a further £500\pounds 500. Work out how much is in the account at the end of 55 years.
Show worked solution

Worked solution

  1. Plan the year-by-year table

    balance→×1.06→+ 500\text{balance} \to \times 1.06 \to +\,500

    Interest first, then the £500 payment, five times over. The exact balance carries forward every year. Exam convention: keep the full unrounded balance in the calculator all the way through and round to the nearest penny only at the very end.

  2. Write the yearly percentage as a multiplier

    100%+6%=106%=1.06100\% + 6\% = 106\% = 1.06

    A 6% increase keeps the whole 100% and adds 6% on top, so multiply by 1.06 each year.

  3. Year 1: add the interest

    £500×1.06=£530\pounds 500 \times 1.06 = \pounds 530

    6% interest on £500 is £30.00, giving £530.

  4. Year 1: add the £500 payment

    £530+500=£1030\pounds 530 + 500 = \pounds 1030

    The payment goes in after the interest, so the balance is £1030.

  5. Year 2: add the interest

    £1030×1.06=£1091.80\pounds 1030 \times 1.06 = \pounds 1091.80

    6% interest on £1030 is £61.80, giving £1091.80.

  6. Year 2: add the £500 payment

    £1091.80+500=£1591.80\pounds 1091.80 + 500 = \pounds 1591.80

    The payment goes in after the interest, so the balance is £1591.80.

  7. Year 3: add the interest

    £1591.80×1.06≈£1687.31\pounds 1591.80 \times 1.06 \approx \pounds 1687.31

    6% interest on £1591.80 is £95.51, giving £1687.31.

  8. Year 3: add the £500 payment

    £1687.31+500≈£2187.31\pounds 1687.31 + 500 \approx \pounds 2187.31

    The payment goes in after the interest, so the balance is £2187.31.

  9. Year 4: add the interest

    £2187.31×1.06≈£2318.55\pounds 2187.31 \times 1.06 \approx \pounds 2318.55

    6% interest on £2187.31 is £131.24, giving £2318.55.

  10. Year 4: add the £500 payment

    £2318.55+500≈£2818.55\pounds 2318.55 + 500 \approx \pounds 2818.55

    The payment goes in after the interest, so the balance is £2818.55.

  11. Year 5: add the interest

    £2818.55×1.06≈£2987.66\pounds 2818.55 \times 1.06 \approx \pounds 2987.66

    6% interest on £2818.55 is £169.11, giving £2987.66.

  12. Year 5: add the £500 payment

    £2987.66+500≈£3487.66\pounds 2987.66 + 500 \approx \pounds 3487.66

    The payment goes in after the interest, so the balance is £3487.66.

  13. Round to the nearest penny

    £3487.66→£3487.66\pounds 3487.66 \to \pounds 3487.66

    The full-precision balance is rounded to the penny only at the end.

  14. Work out the total she paid in

    500+5×500=£3000500 + 5 \times 500 = \pounds 3000

    She paid in £3000 of her own money altogether.

  15. State the answer

    £3487.66\pounds 3487.66

    After 5 years the account holds £3487.66, of which £487.66 is interest.

Answer
£3487.66\pounds 3487.66

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