Chapter 58: Interest, Savings, and Investments
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Interest, Savings, and Investments with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Unit Rate (a rate per one unit)
- Exchange Rate (the value of one currency expressed in another currency)
- Principal (starting amount saved, invested, or borrowed)
- Interest Rate (percentage used to calculate interest)
- Estimate (a close approximation used to check whether an answer is reasonable)
- Solution (a value or result that satisfies the problem)
- Representation (a way to show mathematics using symbols, diagrams, tables, graphs, or words)
- Reasonableness (whether an answer makes sense in the context of the problem)
How to Learn This Chapter
Read the explanation first, follow the examples one step at a time, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
58.1 Principal
Principal is the starting amount saved, invested, or borrowed. This topic focuses on Principal .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find simple interest on $500 at 5% for 2 years.
- Use I=Prt.
- I=500×0.05×2.
Very beginner explanation: Principal is the starting amount saved, invested, or borrowed. This topic focuses on Principal .
Answer: $50.00
Worked Example 2
Problem: Find simple interest on $1000 at 4% for 3 years.
- Use I=Prt.
- I=1000×0.04×3.
Very beginner explanation: Principal is the starting amount saved, invested, or borrowed. This topic focuses on Principal .
Answer: $120.00
Worked Example 3
Problem: Find simple interest on $750 at 6% for 1 years.
- Use I=Prt.
- I=750×0.06×1.
Very beginner explanation: Principal is the starting amount saved, invested, or borrowed. This topic focuses on Principal .
Answer: $45.00
Worked Example 4
Problem: Find simple interest on $1200 at 3.5% for 4 years.
- Use I=Prt.
- I=1200×0.035×4.
Very beginner explanation: Principal is the starting amount saved, invested, or borrowed. This topic focuses on Principal .
Answer: $168.00
Worked Example 5
Problem: Find simple interest on $2000 at 2.5% for 5 years.
- Use I=Prt.
- I=2000×0.025×5.
Very beginner explanation: Principal is the starting amount saved, invested, or borrowed. This topic focuses on Principal .
Answer: $250.00
Worked Example 6
Problem: Find simple interest on $500 at 5% for 2 years.
- Use I = Prt.
- I = 500 × 0.05 × 2.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $50.00
Worked Example 7
Problem: Find simple interest on $1000 at 4% for 3 years.
- Use I = Prt.
- I = 1000 × 0.04 × 3.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $120.00
Worked Example 8
Problem: Find simple interest on $750 at 6% for 1 years.
- Use I = Prt.
- I = 750 × 0.06 × 1.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $45.00
Worked Example 9
Problem: Find simple interest on $1200 at 3.5% for 4 years.
- Use I = Prt.
- I = 1200 × 0.035 × 4.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $168.00
Worked Example 10
Problem: Find simple interest on $2000 at 2.5% for 5 years.
- Use I = Prt.
- I = 2000 × 0.025 × 5.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $250.00
Practice Exercise
Create one new question about Principal. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
58.2 Interest
Interest is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find simple interest on $500 at 5% for 2 years.
- Use I=Prt.
- I=500×0.05×2.
Very beginner explanation: Interest is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $50.00
Worked Example 2
Problem: Find simple interest on $1000 at 4% for 3 years.
- Use I=Prt.
- I=1000×0.04×3.
Very beginner explanation: Interest is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $120.00
Worked Example 3
Problem: Find simple interest on $750 at 6% for 1 years.
- Use I=Prt.
- I=750×0.06×1.
Very beginner explanation: Interest is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $45.00
Worked Example 4
Problem: Find simple interest on $1200 at 3.5% for 4 years.
- Use I=Prt.
- I=1200×0.035×4.
Very beginner explanation: Interest is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $168.00
Worked Example 5
Problem: Find simple interest on $2000 at 2.5% for 5 years.
- Use I=Prt.
- I=2000×0.025×5.
Very beginner explanation: Interest is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $250.00
Worked Example 6
Problem: Find simple interest on $500 at 5% for 2 years.
- Use I = Prt.
- I = 500 × 0.05 × 2.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $50.00
Worked Example 7
Problem: Find simple interest on $1000 at 4% for 3 years.
- Use I = Prt.
- I = 1000 × 0.04 × 3.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $120.00
Worked Example 8
Problem: Find simple interest on $750 at 6% for 1 years.
- Use I = Prt.
- I = 750 × 0.06 × 1.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $45.00
Worked Example 9
Problem: Find simple interest on $1200 at 3.5% for 4 years.
- Use I = Prt.
- I = 1200 × 0.035 × 4.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $168.00
Worked Example 10
Problem: Find simple interest on $2000 at 2.5% for 5 years.
- Use I = Prt.
- I = 2000 × 0.025 × 5.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $250.00
Practice Exercise
Create one new question about Interest. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
58.3 Interest rate
A rate compares two quantities measured in different units. This topic focuses on Interest rate .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: 120 km in 2 h. Find the unit rate.
- Use rate = distance ÷ time.
- 120÷2=60.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Interest rate .
Answer: 60 km/h
Worked Example 2
Problem: 180 km in 3 h. Find the unit rate.
- Use rate = distance ÷ time.
- 180÷3=60.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Interest rate .
Answer: 60 km/h
Worked Example 3
Problem: 250 km in 5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 250÷5=50.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Interest rate .
Answer: 50 km/h
Worked Example 4
Problem: 72 km in 1.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 72÷1.5=48.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Interest rate .
Answer: 48 km/h
Worked Example 5
Problem: 315 km in 4.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 315÷4.5=70.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Interest rate .
Answer: 70 km/h
Worked Example 6
Problem: 120 km are travelled in 2 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 120 ÷ 2 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 7
Problem: 180 km are travelled in 3 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 180 ÷ 3 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 8
Problem: 240 km are travelled in 4 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 240 ÷ 4 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 9
Problem: 300 km are travelled in 5 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 300 ÷ 5 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 10
Problem: 360 km are travelled in 6 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 360 ÷ 6 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Practice Exercise
Create one new question about Interest rate. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
58.4 Simple interest introduction
Simple interest is calculated only on the original principal using I = Prt. This topic focuses on Simple interest introduction .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find simple interest on $500 at 5% for 2 years.
- Use I=Prt.
- I=500×0.05×2.
Very beginner explanation: Simple interest is calculated only on the original principal using I = Prt. This topic focuses on Simple interest introduction .
Answer: $50.00
Worked Example 2
Problem: Find simple interest on $1000 at 4% for 3 years.
- Use I=Prt.
- I=1000×0.04×3.
Very beginner explanation: Simple interest is calculated only on the original principal using I = Prt. This topic focuses on Simple interest introduction .
Answer: $120.00
Worked Example 3
Problem: Find simple interest on $750 at 6% for 1 years.
- Use I=Prt.
- I=750×0.06×1.
Very beginner explanation: Simple interest is calculated only on the original principal using I = Prt. This topic focuses on Simple interest introduction .
Answer: $45.00
Worked Example 4
Problem: Find simple interest on $1200 at 3.5% for 4 years.
- Use I=Prt.
- I=1200×0.035×4.
Very beginner explanation: Simple interest is calculated only on the original principal using I = Prt. This topic focuses on Simple interest introduction .
Answer: $168.00
Worked Example 5
Problem: Find simple interest on $2000 at 2.5% for 5 years.
- Use I=Prt.
- I=2000×0.025×5.
Very beginner explanation: Simple interest is calculated only on the original principal using I = Prt. This topic focuses on Simple interest introduction .
Answer: $250.00
Worked Example 6
Problem: Find simple interest on $500 at 5% for 2 years.
- Use I = Prt.
- I = 500 × 0.05 × 2.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $50.00
Worked Example 7
Problem: Find simple interest on $1000 at 4% for 3 years.
- Use I = Prt.
- I = 1000 × 0.04 × 3.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $120.00
Worked Example 8
Problem: Find simple interest on $750 at 6% for 1 years.
- Use I = Prt.
- I = 750 × 0.06 × 1.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $45.00
Worked Example 9
Problem: Find simple interest on $1200 at 3.5% for 4 years.
- Use I = Prt.
- I = 1200 × 0.035 × 4.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $168.00
Worked Example 10
Problem: Find simple interest on $2000 at 2.5% for 5 years.
- Use I = Prt.
- I = 2000 × 0.025 × 5.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $250.00
Practice Exercise
Create one new question about Simple interest introduction. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
58.5 I = Prt
I = Prt is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: I = Prt: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: I = Prt is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 2
Problem: I = Prt: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: I = Prt is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 3
Problem: I = Prt: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: I = Prt is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 4
Problem: I = Prt: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: I = Prt is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 5
Problem: I = Prt: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: I = Prt is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 6
Problem: Explain I = Prt in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: I = Prt becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy I = Prt and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: I = Prt becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show I = Prt using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: I = Prt becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a I = Prt problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: I = Prt becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where I = Prt could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: I = Prt becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about I = Prt. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
58.6 Savings accounts
Savings accounts is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find simple interest on $500 at 5% for 2 years.
- Use I=Prt.
- I=500×0.05×2.
Very beginner explanation: Savings accounts is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $50.00
Worked Example 2
Problem: Find simple interest on $1000 at 4% for 3 years.
- Use I=Prt.
- I=1000×0.04×3.
Very beginner explanation: Savings accounts is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $120.00
Worked Example 3
Problem: Find simple interest on $750 at 6% for 1 years.
- Use I=Prt.
- I=750×0.06×1.
Very beginner explanation: Savings accounts is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $45.00
Worked Example 4
Problem: Find simple interest on $1200 at 3.5% for 4 years.
- Use I=Prt.
- I=1200×0.035×4.
Very beginner explanation: Savings accounts is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $168.00
Worked Example 5
Problem: Find simple interest on $2000 at 2.5% for 5 years.
- Use I=Prt.
- I=2000×0.025×5.
Very beginner explanation: Savings accounts is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $250.00
Worked Example 6
Problem: Monthly income is $1500 and spending is $1100. Find monthly savings.
- Savings = income - spending.
- 1500 - 1100 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 7
Problem: Monthly income is $2000 and spending is $1600. Find monthly savings.
- Savings = income - spending.
- 2000 - 1600 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 8
Problem: Monthly income is $1750 and spending is $1350. Find monthly savings.
- Savings = income - spending.
- 1750 - 1350 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 9
Problem: Monthly income is $2200 and spending is $1800. Find monthly savings.
- Savings = income - spending.
- 2200 - 1800 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 10
Problem: Monthly income is $3000 and spending is $2600. Find monthly savings.
- Savings = income - spending.
- 3000 - 2600 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Practice Exercise
Create one new question about Savings accounts. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
58.7 Investment growth introduction
Investment growth introduction is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find simple interest on $500 at 5% for 2 years.
- Use I=Prt.
- I=500×0.05×2.
Very beginner explanation: Investment growth introduction is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $50.00
Worked Example 2
Problem: Find simple interest on $1000 at 4% for 3 years.
- Use I=Prt.
- I=1000×0.04×3.
Very beginner explanation: Investment growth introduction is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $120.00
Worked Example 3
Problem: Find simple interest on $750 at 6% for 1 years.
- Use I=Prt.
- I=750×0.06×1.
Very beginner explanation: Investment growth introduction is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $45.00
Worked Example 4
Problem: Find simple interest on $1200 at 3.5% for 4 years.
- Use I=Prt.
- I=1200×0.035×4.
Very beginner explanation: Investment growth introduction is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $168.00
Worked Example 5
Problem: Find simple interest on $2000 at 2.5% for 5 years.
- Use I=Prt.
- I=2000×0.025×5.
Very beginner explanation: Investment growth introduction is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $250.00
Worked Example 6
Problem: Find simple interest on $500 at 5% for 2 years.
- Use I = Prt.
- I = 500 × 0.05 × 2.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $50.00
Worked Example 7
Problem: Find simple interest on $1000 at 4% for 3 years.
- Use I = Prt.
- I = 1000 × 0.04 × 3.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $120.00
Worked Example 8
Problem: Find simple interest on $750 at 6% for 1 years.
- Use I = Prt.
- I = 750 × 0.06 × 1.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $45.00
Worked Example 9
Problem: Find simple interest on $1200 at 3.5% for 4 years.
- Use I = Prt.
- I = 1200 × 0.035 × 4.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $168.00
Worked Example 10
Problem: Find simple interest on $2000 at 2.5% for 5 years.
- Use I = Prt.
- I = 2000 × 0.025 × 5.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $250.00
Practice Exercise
Create one new question about Investment growth introduction. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
58.8 Comparing interest rates
A rate compares two quantities measured in different units. This topic focuses on Comparing interest rates .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: 120 km in 2 h. Find the unit rate.
- Use rate = distance ÷ time.
- 120÷2=60.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Comparing interest rates .
Answer: 60 km/h
Worked Example 2
Problem: 180 km in 3 h. Find the unit rate.
- Use rate = distance ÷ time.
- 180÷3=60.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Comparing interest rates .
Answer: 60 km/h
Worked Example 3
Problem: 250 km in 5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 250÷5=50.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Comparing interest rates .
Answer: 50 km/h
Worked Example 4
Problem: 72 km in 1.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 72÷1.5=48.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Comparing interest rates .
Answer: 48 km/h
Worked Example 5
Problem: 315 km in 4.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 315÷4.5=70.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Comparing interest rates .
Answer: 70 km/h
Worked Example 6
Problem: 120 km are travelled in 2 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 120 ÷ 2 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 7
Problem: 180 km are travelled in 3 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 180 ÷ 3 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 8
Problem: 240 km are travelled in 4 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 240 ÷ 4 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 9
Problem: 300 km are travelled in 5 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 300 ÷ 5 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 10
Problem: 360 km are travelled in 6 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 360 ÷ 6 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Practice Exercise
Create one new question about Comparing interest rates. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
58.9 Effect of time on savings
Effect of time on savings is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Effect of time on savings: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Effect of time on savings is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 2
Problem: Effect of time on savings: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Effect of time on savings is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 3
Problem: Effect of time on savings: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Effect of time on savings is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 4
Problem: Effect of time on savings: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Effect of time on savings is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 5
Problem: Effect of time on savings: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Effect of time on savings is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 6
Problem: Monthly income is $1500 and spending is $1100. Find monthly savings.
- Savings = income - spending.
- 1500 - 1100 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 7
Problem: Monthly income is $2000 and spending is $1600. Find monthly savings.
- Savings = income - spending.
- 2000 - 1600 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 8
Problem: Monthly income is $1750 and spending is $1350. Find monthly savings.
- Savings = income - spending.
- 1750 - 1350 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 9
Problem: Monthly income is $2200 and spending is $1800. Find monthly savings.
- Savings = income - spending.
- 2200 - 1800 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 10
Problem: Monthly income is $3000 and spending is $2600. Find monthly savings.
- Savings = income - spending.
- 3000 - 2600 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Practice Exercise
Create one new question about Effect of time on savings. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
58.10 Effect of rate on savings
A rate compares two quantities measured in different units. This topic focuses on Effect of rate on savings .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: 120 km in 2 h. Find the unit rate.
- Use rate = distance ÷ time.
- 120÷2=60.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Effect of rate on savings .
Answer: 60 km/h
Worked Example 2
Problem: 180 km in 3 h. Find the unit rate.
- Use rate = distance ÷ time.
- 180÷3=60.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Effect of rate on savings .
Answer: 60 km/h
Worked Example 3
Problem: 250 km in 5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 250÷5=50.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Effect of rate on savings .
Answer: 50 km/h
Worked Example 4
Problem: 72 km in 1.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 72÷1.5=48.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Effect of rate on savings .
Answer: 48 km/h
Worked Example 5
Problem: 315 km in 4.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 315÷4.5=70.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Effect of rate on savings .
Answer: 70 km/h
Worked Example 6
Problem: 120 km are travelled in 2 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 120 ÷ 2 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 7
Problem: 180 km are travelled in 3 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 180 ÷ 3 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 8
Problem: 240 km are travelled in 4 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 240 ÷ 4 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 9
Problem: 300 km are travelled in 5 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 300 ÷ 5 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 10
Problem: 360 km are travelled in 6 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 360 ÷ 6 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Practice Exercise
Create one new question about Effect of rate on savings. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
58.11 Estimating growth
Estimating growth is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Estimating growth: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Estimating growth is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 2
Problem: Estimating growth: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Estimating growth is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 3
Problem: Estimating growth: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Estimating growth is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 4
Problem: Estimating growth: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Estimating growth is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 5
Problem: Estimating growth: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Estimating growth is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 6
Problem: Explain Estimating growth in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Estimating growth becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Estimating growth and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Estimating growth becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Estimating growth using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Estimating growth becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Estimating growth problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Estimating growth becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Estimating growth could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Estimating growth becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Estimating growth. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
58.12 Interest earned
Interest earned is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find simple interest on $500 at 5% for 2 years.
- Use I=Prt.
- I=500×0.05×2.
Very beginner explanation: Interest earned is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $50.00
Worked Example 2
Problem: Find simple interest on $1000 at 4% for 3 years.
- Use I=Prt.
- I=1000×0.04×3.
Very beginner explanation: Interest earned is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $120.00
Worked Example 3
Problem: Find simple interest on $750 at 6% for 1 years.
- Use I=Prt.
- I=750×0.06×1.
Very beginner explanation: Interest earned is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $45.00
Worked Example 4
Problem: Find simple interest on $1200 at 3.5% for 4 years.
- Use I=Prt.
- I=1200×0.035×4.
Very beginner explanation: Interest earned is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $168.00
Worked Example 5
Problem: Find simple interest on $2000 at 2.5% for 5 years.
- Use I=Prt.
- I=2000×0.025×5.
Very beginner explanation: Interest earned is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $250.00
Worked Example 6
Problem: Find simple interest on $500 at 5% for 2 years.
- Use I = Prt.
- I = 500 × 0.05 × 2.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $50.00
Worked Example 7
Problem: Find simple interest on $1000 at 4% for 3 years.
- Use I = Prt.
- I = 1000 × 0.04 × 3.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $120.00
Worked Example 8
Problem: Find simple interest on $750 at 6% for 1 years.
- Use I = Prt.
- I = 750 × 0.06 × 1.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $45.00
Worked Example 9
Problem: Find simple interest on $1200 at 3.5% for 4 years.
- Use I = Prt.
- I = 1200 × 0.035 × 4.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $168.00
Worked Example 10
Problem: Find simple interest on $2000 at 2.5% for 5 years.
- Use I = Prt.
- I = 2000 × 0.025 × 5.
Very beginner explanation: Simple interest is calculated from the original principal, rate, and time.
Answer: $250.00
Practice Exercise
Create one new question about Interest earned. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
58.13 Technology for financial calculations
Technology for financial calculations is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Technology for financial calculations: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Technology for financial calculations is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 2
Problem: Technology for financial calculations: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Technology for financial calculations is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 3
Problem: Technology for financial calculations: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Technology for financial calculations is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 4
Problem: Technology for financial calculations: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Technology for financial calculations is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 5
Problem: Technology for financial calculations: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Technology for financial calculations is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 6
Problem: Explain Technology for financial calculations in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Technology for financial calculations becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Technology for financial calculations and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Technology for financial calculations becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Technology for financial calculations using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Technology for financial calculations becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Technology for financial calculations problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Technology for financial calculations becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Technology for financial calculations could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Technology for financial calculations becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Technology for financial calculations. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
58.14 Real-life savings decisions
Real-life savings decisions is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Real-life savings decisions: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Real-life savings decisions is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 2
Problem: Real-life savings decisions: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Real-life savings decisions is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 3
Problem: Real-life savings decisions: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Real-life savings decisions is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 4
Problem: Real-life savings decisions: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Real-life savings decisions is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 5
Problem: Real-life savings decisions: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Real-life savings decisions is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 6
Problem: Monthly income is $1500 and spending is $1100. Find monthly savings.
- Savings = income - spending.
- 1500 - 1100 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 7
Problem: Monthly income is $2000 and spending is $1600. Find monthly savings.
- Savings = income - spending.
- 2000 - 1600 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 8
Problem: Monthly income is $1750 and spending is $1350. Find monthly savings.
- Savings = income - spending.
- 1750 - 1350 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 9
Problem: Monthly income is $2200 and spending is $1800. Find monthly savings.
- Savings = income - spending.
- 2200 - 1800 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 10
Problem: Monthly income is $3000 and spending is $2600. Find monthly savings.
- Savings = income - spending.
- 3000 - 2600 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Practice Exercise
Create one new question about Real-life savings decisions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
Chapter Notes, Practice, and Common Mistakes
Chapter Notes
- Read the complete question before choosing an operation, formula, graph, or model.
- Write technical words together with their meaning until you are comfortable using them.
- Show all important steps so another student can follow your reasoning.
- Keep units, labels, signs, axes, variables, and mathematical symbols clear.
- Estimate before or after calculating when an estimate can help check reasonableness.
- For real-life problems, explain what the final number means in the situation.
Extra Practice
- Create and solve a new question about Principal . Show your reasoning and check your answer.
- Create and solve a new question about Interest . Show your reasoning and check your answer.
- Create and solve a new question about Interest rate . Show your reasoning and check your answer.
- Create and solve a new question about Simple interest introduction . Show your reasoning and check your answer.
- Create and solve a new question about I = Prt . Show your reasoning and check your answer.
- Create and solve a new question about Savings accounts . Show your reasoning and check your answer.
- Create and solve a new question about Investment growth introduction . Show your reasoning and check your answer.
- Create and solve a new question about Comparing interest rates . Show your reasoning and check your answer.
- Create and solve a new question about Effect of time on savings . Show your reasoning and check your answer.
- Create and solve a new question about Effect of rate on savings . Show your reasoning and check your answer.
- Create and solve a new question about Estimating growth . Show your reasoning and check your answer.
- Create and solve a new question about Interest earned . Show your reasoning and check your answer.
Common Mistakes
- Reversing an exchange-rate calculation.
- Comparing financial options without including fees.
- Treating interest rate as a whole number instead of a decimal in calculations.
- Ignoring time when comparing savings or borrowing.
- Giving a number without explaining what it means.
30 Review Questions and Answers
Q1. What is important to remember about Principal?
Answer: Principal is the starting amount saved, invested, or borrowed. This topic focuses on Principal.
Q2. What is important to remember about Interest?
Answer: Interest is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q3. What is important to remember about Interest rate?
Answer: A rate compares two quantities measured in different units. This topic focuses on Interest rate.
Q4. What is important to remember about Simple interest introduction?
Answer: Simple interest is calculated only on the original principal using I = Prt. This topic focuses on Simple interest introduction.
Q5. What is important to remember about I = Prt?
Answer: I = Prt is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q6. What is important to remember about Savings accounts?
Answer: Savings accounts is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q7. What is important to remember about Investment growth introduction?
Answer: Investment growth introduction is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q8. What is important to remember about Comparing interest rates?
Answer: A rate compares two quantities measured in different units. This topic focuses on Comparing interest rates.
Q9. What is important to remember about Effect of time on savings?
Answer: Effect of time on savings is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q10. What is important to remember about Effect of rate on savings?
Answer: A rate compares two quantities measured in different units. This topic focuses on Effect of rate on savings.
Q11. What is important to remember about Estimating growth?
Answer: Estimating growth is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q12. What is important to remember about Interest earned?
Answer: Interest earned is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q13. What is important to remember about Technology for financial calculations?
Answer: Technology for financial calculations is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q14. What is important to remember about Real-life savings decisions?
Answer: Real-life savings decisions is an important Grade 7 idea in Interest, Savings, and Investments. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q15. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q16. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q17. Why do units matter?
Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.
Q18. When should you round?
Answer: Usually round near the end of a calculation unless the question specifically asks for earlier rounding.
Q19. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.
Q20. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the relationship connecting them.
Q21. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q22. What should you do if an answer seems unreasonable?
Answer: Re-read the question, check copied values, signs, units, formulas, and calculations.
Q23. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.
Q24. Why are tables useful?
Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.
Q25. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer you obtained.
Q26. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.
Q27. How should you study this chapter?
Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.
Q28. When is a calculator useful?
Answer: A calculator is useful for lengthy arithmetic after you understand the mathematical setup and can estimate the expected size of the answer.
Q29. Why compare more than one strategy?
Answer: Different strategies can make a problem easier and provide a way to verify the result.
Q30. What is a mathematical model?
Answer: It is a simplified mathematical representation of a real situation used to analyze, explain, or predict.