Simple And Compound Interest

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수업 노트

Simple Interest

Interest is money added regularly to an original amount; with simple interest, each payment is the same because it is based only on the starting amount.
To calculate total simple interest: find a percentage (rate) of the starting amount using a multiplier, then multiply by the number of time periods.
Total balance = starting amount + total interest earned.
Example: $250 at 4% per year for 6 years → interest per year = 0.04 × 250 = $10, total interest = 10 × 6 = $60, final balance = 250 + 60 = $310.
To find the interest rate when given total interest: divide total interest by number of years, then find what percentage that is of the original amount.
Always check if the question asks for the interest earned or the total amount at the end.

Compound Interest

Compound interest is calculated on the running total, not just the starting amount, so interest is earned on previously earned interest.
To calculate compound interest, use a multiplier for the percentage increase and apply it repeatedly for each time period.
For an increase of r% per year, the multiplier is (1 + r/100). Final amount = P × (multiplier)ⁿ, where P is the original amount and n is the number of years.
Example: $1200 at 4% per year for 7 years → multiplier = 1.04, final amount = 1200 × 1.04⁷ ≈ $1579.
The compound interest formula is: Final balance = P(1 + r/100)ⁿ (not given in exam).
Depreciation uses a multiplier less than 1; e.g., a 15% decrease has multiplier 0.85.

Comparing Simple and Compound Interest

Simple interest grows linearly; compound interest grows exponentially.
For the same rate and time, compound interest yields a higher final amount than simple interest (after the first year).
Over many years, compound interest eventually always gives a greater amount because interest is earned on interest.
Example: $1000 at 10% compound vs 12% simple: after 4 years, compound = 1000×1.1⁴ = $1464.10, simple = 1000 + 1000×0.12×4 = $1480; after 6 years, compound = $1771.56, simple = $1720.

Solving Problems with Simple Interest

To find the rate n% when total amount is known: subtract original to get total interest, divide by years to get annual interest, then find percentage of original.
Example: £9000 invested for 5 years becomes £11700 → total interest = £2700, annual interest = £540, rate = 540/9000 = 0.06 = 6%.
To find time: use total interest = P × (r/100) × t, solve for t.
Always round answers as required (e.g., nearest dollar, nearest hundred).

Solving Problems with Compound Interest

To find the final amount: use multiplier method or formula P(1 + r/100)ⁿ.
To find the number of years to reach a target: use trial and improvement or logarithms (not required at Core level).
Example: $1750 at 6.5% compound → target $2000: try n=2 → 1750×1.065² ≈ $1985, n=3 → 1750×1.065³ ≈ $2114, so at least 3 years.
To find the interest earned: subtract the original amount from the final amount.
Example: $8400 at 3.5% for 2 years → final = 8400×1.035² ≈ $8998.29, interest = $8998.29 - $8400 = $598.29.

Common Mistakes and Tips

Double-check whether the question uses simple or compound interest.
Ensure you answer the exact question: interest earned or total amount?
Round answers appropriately (e.g., to the nearest dollar, nearest cent).
For compound interest, the multiplier is (1 + r/100); for depreciation, it is (1 - r/100).

슬라이드

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연습 문제

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1.Simple interest is calculated on which amount?
Easy
- AThe original amount only
- BThe current balance each year
- CThe total amount at the end
- DThe interest earned each year
2.Ethan invests $6400 at a rate of 2.6% per year simple interest. Calculate the total value of his investment at the end of 3 years.
Easy
- A$6899.20
- B$6656
- C$6720
- D$6998.40
3.Jamie invests $12000 at a rate of 5% per year compound interest. Calculate the value of his investment at the end of 3 years.
Medium
- A$13891.50
- B$13800
- C$12600
- D$13900
4.Jan invests $800 at a rate of 3% per year simple interest. Calculate the value of her investment at the end of 4 years.
Easy
- A$896
- B$824
- C$872
- D$900
5.Sam invests $4500 into a savings account which pays 3.5% compound interest each year. Find the total amount in the account after 6 years.
Medium
- A$5531.65
- B$5445
- C$5670
- D$5590
6.Cody invests $1750 in a savings account which pays 6.5% compound interest each year. How many years will it take for the balance to reach at least $2000?
Medium
- A3 years
- B2 years
- C4 years
- D5 years
7.Trina invests $16000 at a rate of 5% per year compound interest. Work out the value of her investment at the end of 4 years.
Medium
- A$19448.10
- B$19200
- C$16800
- D$20000
8.Gino invests $6000 for 5 years at a rate of 1.2% per year compound interest. Calculate the value of his investment at the end of the 5 years. Give your answer correct to the nearest dollar.
Medium
- A$6369
- B$6360
- C$6372
- D$6000

더 많은 문제

9.Lucia invests $5000 at a rate of 4.5% per year compound interest. Calculate the value of her investment at the end of 7 years.
Medium
- A$6804.31
- B$6575
- C$6825
- D$6575.50
10.Ella invests $4000 for 3 years at a rate of 1.2% per year compound interest. Calculate the value of her investment at the end of the 3 years.
Medium
- A$4145.73
- B$4144
- C$4120
- D$4145
11.Javier invests $750 for 3 years at a rate of 1.8% per year compound interest. Calculate the value of his investment at the end of the 3 years.
Medium
- A$791.22
- B$790.50
- C$795
- D$785
12.Hawa invests $750 at a rate of 3.5% per year compound interest. Calculate the value of his investment at the end of 3 years.
Medium
- A$831.54
- B$828.75
- C$840
- D$775
13.$12000 is invested at a rate of n% per year simple interest. At the end of 3 years the value of the investment is $12900. Find the value of n.
Medium
- A2.5
- B3
- C2
- D1.5
14.Riya invests $30000 at a rate of 2.5% per year compound interest. Calculate the value of her investment at the end of 7 years. Give your answer correct to the nearest dollar.
Medium
- A$35661
- B$35250
- C$35660
- D$35700
15.Six years ago a farmer invested $3750 at a rate of 4% per year compound interest. Calculate the total value of his investment after the 6 years. Give your answer correct to the nearest dollar.
Medium
- A$4744
- B$4650
- C$4745
- D$4750
16.A bank offers simple interest at a rate of 3% per year. If $500 is invested for 4 years, what is the total interest earned?
Easy
- A$60
- B$15
- C$600
- D$45
17.What is the multiplier for an increase of 5% per year?
Easy
- A1.05
- B0.05
- C5.0
- D1.5
18.$2000 is invested at 4% per year compound interest for 2 years. What is the total amount after 2 years?
Medium
- A$2163.20
- B$2080.00
- C$2160.00
- D$2080.40
19.A car worth $15000 depreciates by 12% each year. What is its value after 3 years?
Medium
- A$10222.08
- B$13200.00
- C$11400.00
- D$9600.00
20.Paula invests $600 at a rate of r% per year simple interest. At the end of 10 years, the total interest earned is $90. Find r.
Medium
- A1.5
- B15
- C0.15
- D6
21.Harry invests $800 for 2 years at a rate of 3% per year compound interest. Calculate the amount of interest he receives at the end of the 2 years.
Medium
- A$48.72
- B$48.00
- C$49.00
- D$47.72
22.Tomas borrows $5000 for 3 years at a rate of 2.5% per year compound interest. He pays back the whole amount, with interest, at the end of 3 years. Calculate the total amount he pays back.
Medium
- A$5384.45
- B$5375.00
- C$5384.00
- D$5374.45
23.What is the multiplier for a decrease of 8%?
Easy
- A0.92
- B0.08
- C1.08
- D8.0
24.Kim invests £13000 at a rate of 10% per year simple interest. Calculate the total value after five years.
Easy
- A£19500
- B£14300
- C£13000
- D£1950
25.Kim invests £13000 at a rate of 6% compounded annually. Find the value after four years.
Medium
- A£16412.20
- B£16120.00
- C£16412.00
- D£16120.13
26.A savings account pays 2% compound interest per year. If $1000 is deposited, what is the balance after 3 years?
Medium
- A$1061.21
- B$1060.00
- C$1061.20
- D$1062.00
27.Compound interest is calculated on which amount?
Easy
- AThe current balance
- BThe original amount only
- CThe interest only
- DThe final amount
28.A bank pays 3.5% compound interest per year. If $2000 is invested for 5 years, what is the total amount?
Medium
- A$2375.37
- B$2350.00
- C$2375.00
- D$2350.37
29.Match each term with its correct definition.
Easy
- Simple interest
- Compound interest
- Depreciation
- Multiplier
- Interest calculated only on the original amount
- Interest calculated on the running total
- Decrease in value over time
- The decimal factor used to increase or decrease an amount
30.Order the steps to calculate the total amount after 3 years of compound interest at 5% per year on $1000.
Medium
- Find 1000 × 1.05
- Find the result of 1000 × 1.05³
- Multiply by 1.05 again
- Repeat for the third year
31.Which of the following are true about simple interest? (Select all that apply.)
Medium
- AInterest is calculated on the original amount each year.
- BThe interest amount changes each year.
- CThe total interest is the same each year.
- DSimple interest is always better than compound interest.
32.The multiplier for a decrease of 12% is 0.88.
Easy
True or false?
33.$5000 is invested at 4% per year compound interest. After how many years will the investment first exceed $6000?
Medium
- A4 years
- B5 years
- C6 years
- D7 years
34.Match each percentage change to its correct multiplier.
Easy
- Increase of 8%
- Decrease of 8%
- Increase of 120%
- Decrease of 15%
- 1.08
- 0.92
- 2.20
- 0.85
35.Arrange these investments in order of the total amount after 3 years, from smallest to largest.
Medium
- $1000 at 5% simple interest
- $1000 at 5% compound interest
- $1000 at 4% compound interest
- $1000 at 6% simple interest
36.Which of the following are true about compound interest? (Select all that apply.)
Medium
- AInterest is calculated on the original amount only.
- BThe interest amount increases each year.
- CThe multiplier is always greater than 1 for growth.
- DDepreciation uses a multiplier less than 1.
37.What is the multiplier for an increase of 6% per year?
Easy
- A0.06
- B1.06
- C6
- D0.94
38.A car costs $20000. Its value depreciates by 15% each year. What is its value after 3 years? Give your answer to the nearest dollar.
Medium
- A$12283
- B$12282
- C$11000
- D$11500
39.A car worth $20000 depreciates by 15% each year. What is its value after 2 years? Give your answer to the nearest dollar.
Medium
40.What is the multiplier for an increase of 3.5% per year?
Easy
41.$8400 is invested for 2 years at a rate of 3.5% per year compound interest. Calculate the total amount of interest earned. Give your answer to the nearest cent.
Medium
42.A bank offers simple interest at a rate of 4% per year. If $300 is invested for 5 years, what is the total amount of interest earned?
Easy
43.A savings account pays compound interest at a rate of 3% per year. If $500 is deposited, what is the balance after 2 years?
Medium
44.A car worth $18000 depreciates by 10% each year. What is its value after 3 years? Give your answer to the nearest dollar.
Medium
45.$2000 is invested at simple interest. At the end of 4 years, the total amount in the account is $2400. Find the value of the interest rate r (as a percentage).
Medium
46.$1500 is invested at a rate of 4% per year compound interest. How many years will it take for the investment to first exceed $1800?
Hard
47.A bank account offers simple interest at a rate of 3.5% per year. If $800 is invested for 5 years, calculate the total amount of interest earned.
Easy
48.A car worth $18000 depreciates by 12% each year. Calculate its value after 4 years. Give your answer to the nearest dollar.
Medium
49.Complete the sentence about simple interest.
Easy
Simple interest is calculated only on the ____ amount, not on any interest already earned.
50.Explain what the multiplier would be for a compound interest rate of 4.5% per year, and why.
Medium
51.Lin invests $16000 at a rate of r% per year simple interest. At the end of 5 years, she has a total amount of $17920. Find the value of r.
Medium
52.Explain why the multiplier for a 12% decrease is 0.88, and use it to find the value after 3 years of an item initially worth $500 that depreciates by 12% each year.
Medium
53.A car worth $20000 depreciates by 15% each year. What is its value after 2 years? Give your answer to the nearest dollar.
Medium
- A17340 $
- B14450 $
- C13005 $
- D15895 $
54.$8400 is invested for 2 years at a rate of 3.5% per year compound interest. Calculate the total amount of interest earned. Give your answer to the nearest cent.
Medium
- A538.46 $
- B717.95 $
- C598.29 $
- D658.12 $
55.A bank offers simple interest at a rate of 4% per year. If $300 is invested for 5 years, what is the total amount of interest earned?
Easy
- A72 $
- B60 $
- C66 $
- D54 $
56.A savings account pays compound interest at a rate of 3% per year. If $500 is deposited, what is the balance after 2 years?
Medium
- A583.5 $
- B530.45 $
- C477.4 $
- D636.55 $
57.A car worth $18000 depreciates by 10% each year. What is its value after 3 years? Give your answer to the nearest dollar.
Medium
- A14434 $
- B15746 $
- C13122 $
- D11810 $
58.$2000 is invested at simple interest. At the end of 4 years, the total amount in the account is $2400. Find the value of the interest rate r (as a percentage).
Medium
- A4 %
- B5 %
- C7 %
- D6 %
59.$1500 is invested at a rate of 4% per year compound interest. How many years will it take for the investment to first exceed $1800?
Hard
- A6 years
- B5 years
- C4 years
- D7 years
60.A bank account offers simple interest at a rate of 3.5% per year. If $800 is invested for 5 years, calculate the total amount of interest earned.
Easy
- A168 $
- B140 $
- C126 $
- D154 $
61.A car worth $18000 depreciates by 12% each year. Calculate its value after 4 years. Give your answer to the nearest dollar.
Medium
- A12955 $
- B10795 $
- C9715 $
- D11875 $

복습 노트

## Simple & Compound Interest (Core IGCSE Maths) ### Simple Interest - Interest is calculated **only on the original amount** (principal). - Each interest payment is the same. - **Formula:** Total interest = Principal × (rate/100) × time (years). - **Final amount** = Principal + Total interest. - Example: $6400 at 2.6% for 3 years → Interest = 6400 × 0.026 × 3 = $499.20; Total = $6899.20. ### Compound Interest - Interest is calculated on the **running total** (principal + accumulated interest). - Use a **multiplier**: For r% increase, multiplier = 1 + r/100. - **Final amount** = Principal × (multiplier)^(number of years). - Formula (not given in exam): Final = P × (1 + r/100)^n. - Example: $12000 at 5% for 3 years → multiplier = 1.05; Final = 12000 × 1.05^3 = $13891.50. ### Key Differences - Simple interest: linear growth (same interest each year). - Compound interest: exponential growth (interest on interest). - Compound interest eventually yields more than simple interest for the same rate and time. ### Exam Tips - Check if question asks for **interest earned** or **total amount**. - Round answers as instructed (e.g., nearest dollar). - For compound interest, ensure you apply the multiplier the correct number of times. - To find rate or time, rearrange formulas. ### Depreciation (similar to compound interest but decrease) - Multiplier = 1 - r/100. - Final value = Principal × (multiplier)^n.

Simple Interest: Interest calculated only on the original principal amount, resulting in equal interest payments each period.
Compound Interest: Interest calculated on the principal plus any previously earned interest, causing the amount to grow exponentially.
Principal: The original amount of money invested or borrowed.
Multiplier: A decimal factor used to increase (1 + r/100) or decrease (1 - r/100) an amount by a given percentage.
Depreciation: A decrease in value over time, calculated similarly to compound interest but with a reduction multiplier.

플래시카드

What is simple interest?

Interest calculated only on the original amount; each interest payment is the same.

How do you calculate total simple interest earned?

Find a percentage of the starting amount using a multiplier, then multiply by the number of time periods.

How do you find the total balance after simple interest?

Add the total interest earned to the starting amount.

Ethan invests $6400 at 2.6% per year simple interest. Calculate total value after 3 years.

Interest per year = 6400 × 0.026 = $166.40; total interest = 166.40 × 3 = $499.20; total value = 6400 + 499.20 = $6899.20.

Jan invests $800 at 3% per year simple interest. Calculate value after 4 years.

Interest per year = 800 × 0.03 = $24; total interest = 24 × 4 = $96; value = 800 + 96 = $896.

What is compound interest?

Interest calculated on the running total (original plus accumulated interest), not just the starting amount.

How do you calculate compound interest using a multiplier?

Multiply the original amount by (1 + r/100)ⁿ, where r is the percentage rate and n is the number of periods.

Jamie invests $12000 at 5% per year compound interest. Calculate value after 3 years.

Multiplier = 1.05; value = 12000 × 1.05³ = $13891.50.

Sam invests $4500 at 3.5% compound interest. Find total amount after 6 years.

Multiplier = 1.035; amount = 4500 × 1.035⁶ ≈ $5531.65.

Cody invests $1750 at 6.5% compound interest. How many years to reach at least $2000?

Solve 1750 × 1.065ⁿ ≥ 2000. n = 2 gives $1984.89; n = 3 gives $2113.91. So 3 years.

Trina invests $16000 at 5% per year compound interest. Work out value after 4 years.

Value = 16000 × 1.05⁴ = $19448.10.

Gino invests $6000 for 5 years at 1.2% compound interest. Value to nearest dollar?

Value = 6000 × 1.012⁵ ≈ $6369.43 → $6369.

Lucia invests $5000 at 4.5% compound interest for 7 years. Value?

Value = 5000 × 1.045⁷ ≈ $6803.67.

Ella invests $4000 for 3 years at 1.2% compound interest. Value?

Value = 4000 × 1.012³ ≈ $4145.73.

Javier invests $750 for 3 years at 1.8% compound interest. Value?

Value = 750 × 1.018³ ≈ $791.24.

Hawa invests $750 at 3.5% compound interest for 3 years. Value?

Value = 750 × 1.035³ ≈ $831.55.

$12000 invested at n% simple interest for 3 years becomes $12900. Find n.

Interest = 12900 - 12000 = $900; per year = 900/3 = $300; n = (300/12000)×100 = 2.5%.

Sonia invests $5000 for 6 years. Bank A: 3.5% compound. Bank B: 22% increase at end. Which is better and by how much?

Bank A: 5000×1.035⁶ ≈ $6146.28; Bank B: 5000×1.22 = $6100; Bank A better by $46.28.

Riya invests $30000 at 2.5% compound interest for 7 years. Value to nearest dollar?

Value = 30000 × 1.025⁷ ≈ $35660.57 → $35661.

Six years ago farmer invested $3750 at 4% compound interest. Value after 6 years to nearest dollar?

Value = 3750 × 1.04⁶ ≈ $4744.95 → $4745.

Paula invests $600 at r% simple interest for 10 years, earns $90 interest. Find r.

Interest per year = 90/10 = $9; r = (9/600)×100 = 1.5%.

$8400 invested for 2 years at 3.5% compound interest. Total interest earned?

Final amount = 8400 × 1.035² = $8998.29; interest = 8998.29 - 8400 = $598.29.

Harry invests $800 for 2 years at 3% compound interest. Interest received?

Final amount = 800 × 1.03² = $848.72; interest = 848.72 - 800 = $48.72.

Tomas borrows $5000 for 3 years at 2.5% compound interest. Total payback?

Amount = 5000 × 1.025³ = $5384.45.

Kim invests £13000 at 10% simple interest for 5 years. Total value?

Interest per year = 13000×0.10 = £1300; total interest = 1300×5 = £6500; total = 13000+6500 = £19500.

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