Percentages and ratio · Ages 13–14

Compounding periods worksheet

Part of: Percentages (II)

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Percentages and ratio · Ages 13–14

Numsprite
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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.$39,000 at 8% a year, compounded every 6 months, for 3 years. The amount = $ (to the nearest dollar)
Answer:
2.At 8% a year, compounded every 3 months, for 5 years: each period's rate = %, over periods.
Fill in each blank
Answer:
3.$15,000 at 4% a year, compounded every 6 months, for 2 years. The amount = $ (to the nearest dollar)
Answer:
4.At 8% a year, compounded every 3 months, for 4 years: each period's rate = %, over periods.
Fill in each blank
Answer:
5.$3,000 at 8% a year, compounded every 3 months, for 18 months. The amount = $ (to the nearest dollar)
Answer:
6.$5,000 at 10% a year, compounded every 6 months: the amount after 6 months is $, after a year $, after a year and a half $.
Fill in each blank
Answer:
7.8% a year compounded every 6 months is the same as % a year compounded yearly
Answer:

8.$20,000 at 4% a year, compounded every 6 months, for 2 years. Which expression gives the amount?
- A. 20000 × (1 + 4%)²
- B. 20000 × (1 + 2%)²
- C. 20000 × (1 + 2%)⁴
- D. 20000 × (1 + 4%)⁴
Choose the right answer
Answer:
9.At 12% a year compounded every 6 months, each period's rate is 6%.
True or false?
Answer:
10.At 4% a year compounded every 3 months, each period's rate is 1%.
True or false?
Answer:
11.$2,000 at 10% a year, compounded every 6 months, for 3 years. Which expression gives the amount?
- A. 2000 × (1 + 10%)³
- B. 2000 × (1 + 5%)³
- C. 2000 × (1 + 5%)⁶
- D. 2000 × (1 + 10%)⁶
Choose the right answer
Answer:
12.$5,000 at 4% a year for 5 years. Which way of paying the interest gives the most at the end?
- A. Compounded every 6 months
- B. Compounded yearly
- C. Simple interest
- D. Compounded every 3 months
Choose the right answer
Answer:

13.A company borrows $70,000 at 10% a year, compounded every 6 months, and repays it all after 2 years. To the nearest dollar, how much does it repay?
Working:
Answer:
14.$10,000 at 8% a year, compounded every 6 months, for 18 months. Find the amount: put the steps in order.
- A. Amount = 11248.64
- B. Amount = 10000 × 1.04³
- C. Amount = 10000 × (1 + 4%)³
- D. Rate a period = 8% ÷ 2 = 4%
Write the letters in the right order
Working:
Answer:
15.At 4% a year compounded every 6 months, 2 years of saving compound 4 times.
True or false?
Working:
Answer:
16.May saves $4,000 for 18 months at 8% a year, compounded every 3 months. Each period's rate = %, there are periods, and the amount at the end = $ (to the nearest dollar).
Fill in each blank
Working:
Answer:
17.Chi-keung keeps $5,000 in an account for 4 months at 12% a year, compounded monthly. To the nearest dollar, how much is there at the end?
Working:
Answer:
18.Chi-keung has $50,000 to save for 4 years. Bank A pays 8% a year compounded yearly; Bank B pays 7.9% a year compounded every 6 months. Which ends with more?
- A. Bank B
- B. The same
- C. It depends on the years
- D. Bank A
Choose the right answer
Working:
Answer:

Show the answers and working

Compounding periods worksheet: Answers and working

1. 49,347
Each period earns 8% ÷ 2 = 4%, over 2 × 3 = 6 periods: 39000 × 1.04⁶, about 49347.
2. 2, 20
A year has 12 ÷ 3 = 4 periods: each earns 8% ÷ 4 = 2%, and 5 years make 5 × 4 = 20 periods.
3. 16,236
Each period earns 4% ÷ 2 = 2%, over 2 × 2 = 4 periods: 15000 × 1.02⁴, about 16236.
4. 2, 16
A year has 12 ÷ 3 = 4 periods: each earns 8% ÷ 4 = 2%, and 4 years make 4 × 4 = 16 periods.
5. 3,378
Each period earns 8% ÷ 4 = 2%, and 18 months make 18 ÷ 3 = 6 periods: 3000 × (1 + 2%)⁶, about 3378.
6. 5,250, 5,512.5, 5,788.125
Each period earns 10% ÷ 2 = 5%, times 1.05 every 6 months: 5250, 5512.5, 5788.125. Or in one step: 5000 × 1.05³ = 5788.125.
7. 8.16
Two periods a year at 4% each: (1 + 4%)² = 1 + 8.16%. A little over 8%, because the second period earns interest on the first period's interest.

8. C. 20000 × (1 + 2%)⁴
Each period earns 4% ÷ 2 = 2%, over 2 × 2 = 4 periods: 20000 × (1 + 2%)⁴.
9. True
A year has 12 ÷ 6 = 2 periods, each at 12% ÷ 2 = 6%. 12% is the rate for the whole year.
10. True
A year has 12 ÷ 3 = 4 periods, each at 4% ÷ 4 = 1%. 4% is the rate for the whole year.
11. C. 2000 × (1 + 5%)⁶
Each period earns 10% ÷ 2 = 5%, over 3 × 2 = 6 periods: 2000 × (1 + 5%)⁶.
12. D. Compounded every 3 months
At the same yearly rate, the more often it compounds, the sooner interest joins the principal and earns more: every 3 months gives the most.

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

13. 85,085 dollars
Each period is 10% ÷ 2 = 5%, over 4 periods: 70000 × (1 + 5%)⁴, about 85085.
14. D → C → B → A
The rate a period first; 18 months make 18 ÷ 6 = 3 periods; then the formula.
15. True
It compounds 12 ÷ 6 = 2 times a year, so 2 × 2 = 4 times in 2 years.
16. 2, 6, 4,505
Each period earns 8% ÷ 4 = 2%, over 18 ÷ 3 = 6 periods: 4000 × (1 + 2%)⁶, about 4505.
17. 5,203 dollars
Each month earns 12% ÷ 12 = 1%, over 4 periods: 5000 × 1.01⁴, about 5203.
18. A. Bank B
Compare the real yearly rates: Bank A 8%; Bank B (1 + 7.9% ÷ 2)² − 1 = 8.056025%.

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