Compound growth and decay

The Maths Habit

  1. £400 invested at 5% simple interest for 3 years. Find the interest.

    £60

  2. £1500 invested at 2% simple interest for 4 years. What is it worth at the end?

    £1620

  3. £250 invested at 3.5% simple interest for 2 years. Find the interest.

    £17.50

Would you rather have £1 million today, or 1p that doubles every day for 30 days?

The penny: it passes £5 million

Write the multiplier

  1. Grows by 4%

    1.04

  2. Falls by 15%

    0.85

  3. Grows by 12%

    1.12

  4. Falls by 3%

    0.97

Compound
Each change is worked out on the new amount, not the amount at the start.

£200 grows by 10% each year

£200

£600 is invested. It grows by 5% each year. Work out its value after 3 years.

× 1.05× 1.05× 1.05£600→£630→£661.50→£694.58StartYear 1Year 2Year 3
Answer£694.58

£900 is invested. It grows by 2% each year. Work out its value after 3 years.

× 1.02× 1.02× 1.02£900→£918→£936.36→£955.09StartYear 1Year 2Year 3
Answer£955.09

£600 is invested. It grows by 5% each year. Work out its value after 3 years.

× 1.05× 1.05× 1.05£600→£630→£661.50→£694.58StartYear 1Year 2Year 3
Answer£694.58

£1200 is invested. It grows by 4% each year. Work out its value after 3 years.

× 1.04× 1.04× 1.04£1200→£1248→£1297.92→£1349.84StartYear 1Year 2Year 3
Answer£1349.84

£3000 is invested. It grows by 1.5% each year.
Work out its value after 6 years.

A van is worth £8000. It falls by 10% each year. Work out its value after 3 years.

× 0.9× 0.9× 0.9£8000→£7200→£6480→£5832StartYear 1Year 2Year 3
Answer£5832

A phone is worth £500. It falls by 20% each year. Work out its value after 3 years.

× 0.8× 0.8× 0.8£500→£400→£320→£256StartYear 1Year 2Year 3
Answer£256

A van is worth £8000. It falls by 10% each year. Work out its value after 3 years.

× 0.9× 0.9× 0.9£8000→£7200→£6480→£5832StartYear 1Year 2Year 3
Answer£5832

A boat is worth £15 000. It falls by 12% each year. Work out its value after 2 years.

× 0.88× 0.88£15 000→£13 200→£11 616StartYear 1Year 2
Answer£11 616

A van is worth £8000. It falls by 10% each year. Work out its value after 3 years.

× 0.9× 0.9× 0.9£8000→£7200→£6480→£5832StartYear 1Year 2Year 3
Answer£5832

£2500 is invested. It grows by 3% each year. Work out its value after 3 years.

× 1.03× 1.03× 1.03£2500→£2575→£2652.25→£2731.82StartYear 1Year 2Year 3
Answer£2731.82

A van is worth £8000. It falls by 10% each year. Work out its value after 3 years.

× 0.9× 0.9× 0.9£8000→£7200→£6480→£5832StartYear 1Year 2Year 3
Answer£5832

A bike is worth £750. It falls by 30% each year. Work out its value after 3 years.

× 0.7× 0.7× 0.7£750→£525→£367.50→£257.25StartYear 1Year 2Year 3
Answer£257.25

A van is worth £8000. It falls by 10% each year. Work out its value after 3 years.

× 0.9× 0.9× 0.9£8000→£7200→£6480→£5832StartYear 1Year 2Year 3
Answer£5832

A painting is worth £4000. Its value rises by 6% each year. Work out its value after 2 years.

× 1.06× 1.06£4000→£4240→£4494.40StartYear 1Year 2
Answer£4494.40

Compound growth and decay worksheet, page 1

Compound growth and decay worksheet, page 2

Answer sheet

  1. £1000 is invested and grows by 5% each year. After how many years is it first worth more than £1500?

    9 years

  2. A colony of 200 bacteria doubles every hour. How many bacteria are there after 6 hours?

    12 800

1p doubles every day. Write the calculation for its value on day 30.

0.01 × 229 = £5 368 709.12

  1. £800 is invested. It grows by 3% each year. Work out its value after 2 years.

    £848.72

  2. A car is worth £9000. It falls by 15% each year. Work out its value after 3 years.

    £5527.13

  3. £2000 is invested. It grows by 4% each year. After how many years is it first worth more than £2400?

    5 years
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