Percentages and ratio · Ages 13–14

Compound interest worksheet

Part of: Percentages (II)

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Percentages and ratio · Ages 13–14

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Name:Date:Score:／48

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

1.$5,000 at 5% a year, compounded yearly: the amount after 1 year is $, after 2 years $, after 3 years $.
Fill in each blank
Answer:
2.$30,000 at 10% a year, compounded yearly, for 6 years. The amount = $ (to the nearest dollar)
Answer:
3.$29,000 at 8% a year, compounded yearly, for 5 years. The amount = $ (to the nearest dollar)
Answer:
4.$20,000 at 4% a year, compounded yearly, for 5 years: the compound interest = $ (to the nearest dollar)
Answer:
5.$32,000 at 4% a year, compounded yearly, for 4 years: the compound interest = $ (to the nearest dollar)
Answer:
6.At 10% a year, compounded yearly, the amount after 4 years is $40,994.8. The principal = $
Answer:
7.$52,000 at 6% a year, compounded yearly, for 6 years, to the nearest dollar: the amount is $, the interest $, which is $ more than simple interest.
Fill in each blank
Answer:
8.At 5% a year, compounded yearly, the amount after 3 years is $50,935.5. The principal = $
Answer:

9.A principal of $10,000 at 6% a year, compounded yearly. Which expression gives the amount after 8 years?
- A. 10000 × 0.06⁸
- B. 10000 × 1.06⁸
- C. 10000 × (1 + 6% × 8)
- D. 10000 × 1.06 × 8
Choose the right answer
Answer:
10.$10,000 at 6% a year for 5 years. How much more does interest compounded yearly earn than simple interest, to the nearest dollar?
- A. $3,000
- B. $13,382
- C. $3,382
- D. $382
Choose the right answer
Answer:
11.On $20,000 at 4% a year, compounded yearly, the interest for 5 years is about $4,000.
True or false?
Answer:
12.$50,000 at 4% a year for 5 years. How much more does interest compounded yearly earn than simple interest, to the nearest dollar?
- A. $10,833
- B. $833
- C. $10,000
- D. $60,833
Choose the right answer
Answer:

13.Tsz-hin's parents put away $35,000 for Tsz-hin at 5% a year, compounded yearly. To the nearest dollar, how much is there after 8 years?
Working:
Answer:
14.Ka-lok's sister borrows $56,000 at 3% a year, compounded yearly, and pays it all back after 4 years (to the nearest dollar). She repays $, of which $ is interest.
Fill in each blank
Working:
Answer:
15.A deposit earns 10% a year, compounded yearly, and grows to $53,240 after 3 years. What was put in?
Working:
Answer:
16.Ka-lok has $20,000 to save for 2 years. Bank A pays 12% a year simple interest; Bank B pays 10% a year compounded yearly. Which pays more interest?
- A. They pay the same
- B. Bank A
- C. It depends on the money put in
- D. Bank B
Choose the right answer
Working:
Answer:
17.At 10% a year, compounded yearly, the amount after 4 years is $29,282. Find the principal P: put the steps in order.
- A. P = 29282 ÷ 1.1⁴
- B. P × (1 + 10%)⁴ = 29282
- C. P × 1.1⁴ = 29282
- D. P = 20000
Write the letters in the right order
Working:
Answer:
18.Ka-yan puts $20,000 in the bank at 5% a year, compounded yearly. For at least how many whole years must it stay to grow past $26,000?
Working:
Answer:

Show the answers and working

Compound interest worksheet: Answers and working

1. 5,250, 5,512.5, 5,788.125
Times 1.05 each year: 5000 × 1.05 = 5250, 5250 × 1.05 = 5512.5, 5512.5 × 1.05 = 5788.125. Or in one step: 5000 × 1.05³ = 5788.125.
2. 53,147
Amount = 30000 × (1 + 10%)⁶ = 30000 × 1.1⁶, about 53147. Round at the last step only.
3. 42,611
Amount = 29000 × (1 + 8%)⁵ = 29000 × 1.08⁵, about 42611. Round at the last step only.
4. 4,333
The amount first, 20000 × 1.04⁵, then take off the principal, 20000: about 4333.
5. 5,435
The amount first, 32000 × 1.04⁴, then take off the principal, 32000: about 5435.
6. 28,000
Principal × 1.1⁴ = 40994.8, so the principal = 40994.8 ÷ 1.1⁴ = 28000. Not 40994.8 × (1 − 10%)⁴.
7. 73,763, 21,763, 3,043
Amount = 52000 × 1.06⁶, about 73763; interest = 73763 − 52000 = 21763; simple interest = 52000 × 6% × 6 = 18720, 3043 less.
8. 44,000
Principal × 1.05³ = 50935.5, so the principal = 50935.5 ÷ 1.05³ = 44000. Not 50935.5 × (1 − 5%)³.

9. B. 10000 × 1.06⁸
Each year the money becomes 1.06 times the year before; 8 years multiply 8 times: 10000 × 1.06⁸.
10. D. $382
Compound interest = 10000 × 1.06⁵ − 10000, about 3382; simple interest = 10000 × 6% × 5 = 3000; the gap is about 382.
11. False
Compound interest = 20000 × 1.04⁵ − 20000, about 4333. $4,000 is simple interest, each year on the principal alone.
12. B. $833
Compound interest = 50000 × 1.04⁵ − 50000, about 10833; simple interest = 50000 × 4% × 5 = 10000; the gap is about 833.

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

13. 51,711 dollars
35000 × (1 + 5%)⁸ = 35000 × 1.05⁸, about 51711.
14. 63,028, 7,028
56000 × 1.03⁴, about 63028; interest = 63028 − 56000 = 7028.
15. 40,000 dollars
Principal × 1.1³ = 53240, so the principal = 53240 ÷ 1.1³ = 40000.
16. B. Bank A
Bank A: 20000 × 12% × 2 = 4800; Bank B: 20000 × 1.1² − 20000, about 4200.
17. B → C → A → D
Write the amount's formula, turn 1 + 10% into 1.1, then divide both sides by 1.1⁴.
18. 6 years
Times 1.05 year by year: 20000 × 1.05⁵ hasn't passed 26000 yet, 20000 × 1.05⁶ has, so 6 years.

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