Introduction
Simple Interest: Earning and Paying Interest is an important Grade 7 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with simple interest: earning and paying interest.
What Is Simple Interest: Earning and Paying Interest?
Simple Interest: Earning and Paying Interest means choosing a model, naming what each number means, and explaining the strategy.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding Simple Interest: Earning and Paying Interest
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Read the question carefully and identify what is being asked.
- Choose a model, equation, table, or diagram that matches the situation.
- Solve one step at a time and keep units or labels attached.
- Use the answer explanation to check that the result makes sense.
Visual Models
Visual Model 1
Question: Based on the table above, how much interest will be earned?
| Principal | Rate | Time (years) | Interest |
|---|---|---|---|
| $\(500\) | \(3%\) | \(2\) | ? |
- A. \($15\)
- B. \($60\)
- C. \($45\)
- D. \($30\)
Why it works: \(I=500\times0.03\times2=$30\).
Answer: \($30\)
Visual Model 2
Question: What will be the total amount after the time period?
| Principal | Rate | Time (years) | Total Amount |
|---|---|---|---|
| $\(2000\) | \(5.5%\) | \(3\) | ? |
- A. \($2275\)
- B. \($3300\)
- C. \($2360\)
- D. \($2330\)
Why it works: \(I=2000\times0.055\times3=$330\). \(A=2000+330=$2330\).
Answer: \($2330\)
Worked Examples
Example 1
Question: Which account earns more interest, and by how much?
| Scenario | Principal | Annual Rate | Years |
|---|---|---|---|
| Account 1 | $\(1000\) | \(6%\) | \(2\) |
| Account 2 | $\(1200\) | \(4%\) | \(2\) |
- A. Account 1 by \($20\)
- B. Account 2 by \($20\)
- C. Account 1 by \($24\)
- D. Both earn the same
- Account 1: \(I=1000(0.06)(2)=$120\).
- Account 2: \(I=1200(0.04)(2)=$96\).
- Difference: \(120-96=$24\).
Answer: Account 1 by \($24\)
Example 2
Question: Based on the table, what is the annual interest rate?
- A. \(2.5\%\)
- B. \(10\%\)
- C. \(7.5\%\)
- D. \(5\%\)
- Each year adds \($50\) interest on principal of \($1000\): rate \(=\frac{50}{1000}=0.05=5\%\).
Answer: \(5\%\)
Example 3
Question: The graph shows a balance growing with simple interest. What is the annual interest earned?
- A. \($250\) per year
- B. \($1000\) per year
- C. \($625\) per year
- D. \($500\) per year
- The line is linear; from year 0 to year 1, balance goes from \($2000\) to \($2500\) (gain of \($500\)).
Answer: \($500\) per year
Real-World Word Problems
Problem 1
Question: A savings account earns \($75\) in interest from a principal of \($500\) at an annual rate of \(5\%\). How many years has the money been in the account?
- A. \(1.5\) years
- B. \(2\) years
- C. \(2.5\) years
- D. \(3\) years
Why it works: Using \(I=Prt\): \(75=500\times0.05\times t \Rightarrow 75=25t \Rightarrow t=3\).
Answer: \(3\) years
Problem 2
Question: A student borrows \($2500\) for a bike at \(9\%\) simple interest per year. If the loan must be repaid in \(18\) months, how much interest will the student pay?
- A. \($225\)
- B. \($675\)
- C. \($450\)
- D. \($337.50\)
Why it works: STEP 1: Convert \(18\) months to years: \(t = 18 \div 12 = 1.5\) years. STEP 2: \(I=2500\times0.09\times1.5=$337.50\).
Answer: \($337.50\)
Common Mistakes
- Rushing before identifying what the numbers represent.
- Choosing an operation that does not match the situation.
- Dropping labels, units, or context from the answer.
- Skipping the estimate or reasonableness check.
Strategy Tips
- Underline the question being asked.
- Use a model before jumping to computation.
- Write an equation that matches the story or picture.
- Explain the final answer in a sentence.
Practice Questions
Question 1
Using the simple interest formula \(I=Prt\), how much interest does \($800\) earn at an annual rate of \(5\%\) over \(3\) years?
- A. \($40\)
- B. \($240\)
- C. \($125\)
- D. \($120\)
Question 2
Maya deposits \($1200\) into a savings account with a simple interest rate of \(4\%\) per year. How much interest will she earn after \(2\) years?
- A. \($48\)
- B. \($240\)
- C. \($144\)
- D. \($96\)
Question 3
A loan of \($5000\) has a simple interest rate of \(6\%\) per year. What will be the total amount owed after \(4\) years?
- A. \($5600\)
- B. \($6000\)
- C. \($6200\)
- D. \($7000\)
Question 4
Jordan invests \($2000\) at a simple interest rate of \(3.5\%\) per year for \(5\) years. How much interest will he earn?
- A. \($70\)
- B. \($175\)
- C. \($350\)
- D. \($700\)
Question 5
An investment of \($3000\) earns \($270\) in simple interest over \(2\) years. What is the annual interest rate?
- A. \(3\%\)
- B. \(9\%\)
- C. \(5\%\)
- D. \(4.5\%\)
Question 6
A car loan of \($15000\) is taken at a simple interest rate of \(7\%\) per year. How much total interest will be paid over \(6\) years?
- A. \($4500\)
- B. \($10500\)
- C. \($7000\)
- D. \($6300\)
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \($120\)
\(I=Prt=800\times0.05\times3=$120\).
Question 2
Answer: \($96\)
STEP 1: Convert percentage to decimal: \(4\% = 4 \div 100 = 0.04\). STEP 2: \(I=1200\times0.04\times2=$96\).
Question 3
Answer: \($6200\)
First find interest: \(I=5000\times0.06\times4=$1200\). Then \(A=P+I=5000+1200=$6200\).
Question 4
Answer: \($350\)
\(I=2000\times0.035\times5=$350\). Convert \(3.5\%\) to \(0.035\).
Question 5
Answer: \(4.5\%\)
\(270=3000\times r\times2 \Rightarrow 270=6000r \Rightarrow r=0.045=4.5\%\).
Question 6
Answer: \($6300\)
\(I=15000\times0.07\times6=$6300\).
Connection to Standards
This lesson supports Grade 7 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
Simple Interest: Earning and Paying Interest becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Understand the model before choosing the operation.
