Chapter 6: Review

The chapter problem, solved

The account starts with £600 and earns 4% compound interest each year. The multiplier is 1.04, so after two years:

The balance is £648.96, which is more than £640. The estimate was close enough to predict the direction, and the exact method gives the balance.

Mixed practice — choose the method first

For each question, choose a method before calculating. The practice mixes percentages with methods from earlier chapters.

1. Work out 10% of £360.
2. Work out 25% of 84.
3. Work out 15% of £240.
4. Write 37% as a fraction in its simplest form.
5. Work out $3/8$ of 144.
6. A £68 jacket has a 20% discount. Work out the discount amount.
7. A worker earns 6% commission on sales of £1,250. Work out the commission.
8. A learner works out 12% of 250 by finding 10% and 2%. Work out both parts and the total.
9. A recipe uses 450 g of flour. Work out 40% of this amount.

10. Work out 17.5% of 320.

11. Increase £80 by 15%.

12. Decrease 240 by 12%.
13. A price rises from £40 to £46. Work out the percentage increase.
14. A quantity falls from 250 to 200. Work out the percentage decrease.
15. Write the multiplier for a 7% increase.
16. Write the multiplier for a 35% decrease.
17. A £560 bicycle is reduced by 8%. Work out its new price.
18. A town population of 18 000 increases by 2.5%. Work out the new population.
19. A value changes from 64 to 80. Work out the percentage change and state whether it is an increase or decrease.

20. A £120 item increases by 10%, then decreases by 10%. Work out its final price.

21. After a 20% discount, a coat costs £72. Work out its original price.

22. A value after a 15% increase is 92. Work out its original value.
23. A price including 20% VAT is £54. Work out the price before VAT.
24. A value is reduced by 30% and is now 84. Work out its original value.
25. A television costs £408 after a 15% reduction. Work out the price before the reduction.
26. A value rises from an unknown amount to £138. The increase is 15%. Work out the starting value.
27. A number after a 12% decrease is 220. Work out the original number.
28. A learner subtracts 20% of £80 from £80 to reverse a 20% reduction. Explain the error and find the original if the reduced value is £80.
29. H H A price after 5% VAT is £210. Work out the price before VAT.

30. A phone is sold for £315 after a 30% discount. Work out its marked price.

31. £500 is invested at 4% simple interest each year for 3 years. Work out the interest.

32. £750 is invested at 2% simple interest each year for 5 years. Work out the final amount.
33. £600 is invested at 5% compound interest for 2 years. Work out the final amount.
34. Write the multiplier for 3% interest, compounded yearly.
35. Find the final amount for £1000 at 6% for 2 years using simple interest, then compound interest.
36. £2400 is invested at 3.5% simple interest for 4 years. Work out the interest and final amount.
37. £1250 is invested at 2.4% compound interest for 3 years. Give the final amount to the nearest penny.
38. A savings account pays 4% compound interest. Work out the balance of £800 after 4 years.
39. Explain why compound interest gives more than simple interest after several years at a positive rate.

40. £900 is invested at 3% compound interest for 5 years. Work out the increase in value to the nearest penny.

41. A population of 2400 grows by 3% each year for 4 years. Work out the population, to the nearest whole person.

42. A machine worth £8000 loses 12% of its value each year. Work out its value after 3 years.
43. A quantity starts at 500 and increases by 8%, then by 6%. Work out the final quantity.
44. A value is multiplied by 0.72. State the percentage decrease.
45. A £4000 investment grows to £4410 in 2 years with annual compound growth. Find the annual percentage rate.
46. A car worth £18 000 depreciates by 18% each year. Work out its value after 2 years.
47. A £1000 amount grows by 10% then falls by 10%. Work out the final amount and compare it with £1000.
48. A population of 5000 grows by 2% each year. Work out its population after 10 years, to the nearest whole person.
49. An investment doubles in 12 years with annual compound growth. Find the annual multiplier to 3 significant figures.
50. A substance decays by 7% each hour. What percentage remains after 5 hours?

What you can now do

• find a percentage of an amount and calculate percentage change;
• reverse a percentage change to recover an original amount;
• compare simple and compound interest;
• model repeated growth and decay with a multiplier.

Your relevance reflection

Return to the example you wrote at the start. What percentage calculation would help in that situation? Has your view of the situation changed after learning these methods?