Percentages and ratio · Ages 13–14

Growth and depreciation worksheet

Part of: Percentages (II)

In the print window, choose “Save as PDF” to download it. The answers print on the last page.

Percentages and ratio · Ages 13–14

Numsprite
numsprite.com

Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

1.Losing 20% a year: after 3 years the value is % of the first, so % has gone in all.
Fill in each blank
Answer:
2.A city of 90000 people grows 4% a year. To the nearest whole number, how many people will it have after 4 years?
Answer:
3.A city of 260000 people grows 5% a year. To the nearest whole number, how many people will it have after 3 years?
Answer:
4.A machine loses 10% of its value a year and is worth $295,245 after 4 years. What was it worth new?
Answer:
5.A machine loses 20% of its value a year and is worth $204,800 after 3 years. What was it worth new?
Answer:
6.A new car worth $100,000 loses 15% of its value in its first year and 12% a year after that. To the nearest dollar, what is it worth after 3 years?
Answer:
7.A new car worth $160,000 loses 25% of its value in its first year and 8% a year after that. To the nearest dollar, what is it worth after 4 years?
Answer:

8.A number grows 50% a year, so in 4 years it has grown 200% in all.
True or false?
Answer:
9.A machine loses 20% of its value each year. After 3 years, its value is its first value times which of these?
- A. 0.8 × 3
- B. 0.8³
- C. 0.2³
- D. 1 − 0.2 × 3
Choose the right answer
Answer:
10.A number grows 20% a year, so in 4 years it has grown 80% in all.
True or false?
Answer:
11.A machine loses 10% of its value each year. After 7 years, its value is its first value times which of these?
- A. 0.1⁷
- B. 1 − 0.1 × 7
- C. 0.9⁷
- D. 0.9 × 7
Choose the right answer
Answer:
12.A website has 10000 members, and the number grows 10% a year. At the end of which year does it first pass 20000?
- A. The end of year 10
- B. The end of year 8
- C. The end of year 7
- D. The end of year 9
Choose the right answer
Answer:

13.A new town has 270000 people and is expected to grow 2% a year. To the nearest whole number, after 4 years it will have people, more than now.
Fill in each blank
Working:
Answer:
14.A lake has 2000 fish, and the number falls 25% a year. After at least how many whole years are there fewer than 1000?
Working:
Answer:
15.May's dad bought a car for $460,000, and it loses 20% of its value a year. To the nearest dollar, what is it worth after 4 years?
Working:
Answer:
16.A flat's value rises 10% a year for 4 years, then falls 15% a year for 4 years, and ends higher than it began.
True or false?
Working:
Answer:
17.A company's sales grew 10% a year for 4 years in a row, to $1,010,229 this year. What were they 4 years ago?
Working:
Answer:
18.A machine loses 20% of its value a year and is worth $118,784 after 4 years. With its first value $x, find x: put the steps in order.
- A. x = 290000
- B. x = 118784 ÷ 0.8⁴
- C. x × 0.8⁴ = 118784
- D. x × (1 − 20%)⁴ = 118784
Write the letters in the right order
Working:
Answer:

Show the answers and working

Growth and depreciation worksheet: Answers and working

1. 51.2, 48.8
Each year leaves 0.8: 0.8³, that is 51.2% of the first value, so 100% − 51.2% = 48.8% has gone, not 3 × 20% = 60%.
2. 105287 people
90000 × (1 + 4%)⁴ = 90000 × 1.04⁴, about 105287 people.
3. 300983 people
260000 × (1 + 5%)³ = 260000 × 1.05³, about 300983 people.
4. 450,000 dollars
First value × 0.9⁴ = 295245, so it was 295245 ÷ 0.9⁴ = 450000. Not 295245 × (1 + 10%)⁴.
5. 400,000 dollars
First value × 0.8³ = 204800, so it was 204800 ÷ 0.8³ = 400000. Not 204800 × (1 + 20%)³.
6. 65,824 dollars
The first year leaves 1 − 15%, each of the next 2 years 1 − 12%: 100000 × (1 − 15%) × (1 − 12%)², about 65824.
7. 93,443 dollars
The first year leaves 1 − 25%, each of the next 3 years 1 − 8%: 160000 × (1 − 25%) × (1 − 8%)³, about 93443.

8. False
Multiply: 1.5⁴ = 1 + 406.25%, a 406.25% rise. Each year's 50% is of the year before's bigger value, so it beats 4 × 50% = 200%.
9. B. 0.8³
Each year leaves 1 − 20% = 0.8 of it; over 3 years, 0.8³.
10. False
Multiply: 1.2⁴ = 1 + 107.36%, a 107.36% rise. Each year's 20% is of the year before's bigger value, so it beats 4 × 20% = 80%.
11. C. 0.9⁷
Each year leaves 1 − 10% = 0.9 of it; over 7 years, 0.9⁷.
12. B. The end of year 8
Multiply by 1.1 year by year until it passes 20000: 10000 × 1.1⁷ hasn't, 10000 × 1.1⁸ has.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 292257, 22257
270000 × 1.02⁴, about 292257 people; 292257 − 270000 = 22257 more.
14. 3 years
Times 0.75 year by year: 2000 × 0.75² isn't below 1000 yet, 2000 × 0.75³ is, so 3 years.
15. 188,416 dollars
Each year leaves 0.8 of it: 460000 × 0.8⁴, about 188416.
16. False
It ends at 1.1⁴ × 0.85⁴ = (1.1 × 0.85)⁴ = 0.935⁴: higher only if 0.935 is more than 1.
17. 690,000 dollars
The sales then × 1.1⁴ = 1010229, so they were 1010229 ÷ 1.1⁴ = 690000.
18. D → C → B → A
Each year leaves 1 − 20% = 0.8; form the equation, then divide both sides by 0.8⁴.

Numsprite · numsprite.com/en/worksheets/percentages-2/growth-and-depreciation