Introduction
Compound Interest Introduction 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 compound interest introduction.
What Is Compound Interest Introduction?
Compound Interest Introduction 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 Compound Interest Introduction
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: Rosario puts \($900\) in a savings account earning \(8\%\) annual compound interest. The balance for years \(0\), \(1\), \(2\), and \(3\) is shown below. Which year shows the balance first exceeding \($1{,}000\)?
| Year | Balance |
|---|---|
| 0 | $900 |
| 1 | $972 |
| 2 | $1{,}049.76 |
| 3 | $1{,}133.74 |
- A. Year 1
- B. Year 4
- C. Year 3
- D. Year 2
Why it works: From the table, year 1 gives $972 (below $1,000) and year 2 gives $1,049.76 (first to exceed $1,000).
Answer: Year 2
Visual Model 2
Question: The table below shows a savings account with \($400\) earning \(5\%\) annual compound interest: What is the balance at the end of year 2?
| Year | Interest Earned | Balance |
|---|---|---|
| 0 | -- | $400 |
| 1 | $20 | $420 |
| 2 | ? | ? |
| 3 | $23.10 | $506.25 |
- A. \($440\)
- B. \($450\)
- C. \($442\)
- D. \($441\)
Why it works: Year 2 balance: \(420 \times 1.05 = 441\). Interest earned: \(441 - 420 = 21\).
Answer: \($441\)
Worked Examples
Example 1
Question: An account earns interest compounded annually. If the balance grows from \($1{,}000\) to \($1{,}440\) in \(2\) years, what is the annual interest rate?
| Year | Multiplier | Balance |
|---|---|---|
| 0 | -- | $1{,}000 |
| 1 | \((1+r)\) | ? |
| 2 | \((1+r)^2\) | $1{,}440 |
- A. \(20\%\)
- B. \(22\%\)
- C. \(44\%\)
- D. \(50\%\)
- \(1000(1 + r)^2 = 1440 \Rightarrow (1+r)^2 = 1.44 \Rightarrow 1 + r = 1.20 \Rightarrow r = 0.20 = 20\%\).
Answer: \(20\%\)
Example 2
Question: A deposit of \($1{,}500\) earns compound interest. The table shows balances at years 0, 1, 2, and 3. What is the annual interest rate?
| Year | Balance |
|---|---|
| 0 | $1{,}500 |
| 1 | $1{,}650 |
| 2 | $1{,}815 |
| 3 | $1{,}996.50 |
- A. \(8\%\)
- B. \(12\%\)
- C. \(15\%\)
- D. \(10\%\)
- From year 0 to year 1: \(\frac{1650}{1500} = 1.10\), so rate is \(10\%\).
- Verify year 2: \(1650 \times 1.10 = 1815\) ✓
Answer: \(10\%\)
Example 3
Question: A young person invests \($400\) at \(3\%\) annual compound interest and leaves it untouched for \(5\) years. Approximately how much will the account contain?
| Year | Balance |
|---|---|
| 0 | $400.00 |
| 1 | $412.00 |
| 2 | $424.36 |
| 3 | $437.09 |
| 4 | $450.21 |
| 5 | $463.72 |
- A. \($460\)
- B. \($520\)
- C. \($485\)
- D. \($463\)
- \(A = 400(1.03)^5 = 400 \times 1.1593 = 463.72 \approx 463\).
Answer: \($463\)
Real-World Word Problems
Problem 1
Question: A student wants to compare compound interest vs.\ simple interest on \($600\) at \(5\%\) annual rate. After \(3\) years, what is the difference in interest earned?
- A. \($0\) (they are the same)
- B. \($1.58\)
- C. \($4.58\)
- D. \($7.50\)
Why it works: Simple: \(600 \times 0.05 \times 3 = 90\). Compound: \(600(1.05)^3 = 694.58\); interest \(= 94.58\). Difference: \(94.58 - 90 = 4.58\).
Answer: \($4.58\)
Problem 2
Question: A savings account grows from \($600\) to \($684\) in one year with annual compound interest. What is the interest rate?
- A. \(10\%\)
- B. \(12\%\)
- C. \(14\%\)
- D. \(15\%\)
Why it works: \(600(1 + r) = 684 \Rightarrow 1 + r = 1.14 \Rightarrow r = 0.14 = 14\%\).
Answer: \(14\%\)
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
Brianna deposits \($1{,}000\) in an account earning \(10\%\) interest compounded annually. What is the balance after \(2\) years?
- A. \($1{,}100\)
- B. \($1{,}200\)
- C. \($1{,}210\)
- D. \($1{,}220\)
Question 2
Marcus invests \($500\) at \(5\%\) annual compound interest. What is the balance after \(3\) years?
- A. \($575\)
- B. \($578.81\)
- C. \($579.13\)
- D. \($625\)
Question 3
A savings account starts with \($2{,}000\) and earns \(8\%\) interest compounded annually. How much interest is earned after \(2\) years?
- A. \($160\)
- B. \($320\)
- C. \($331.20\)
- D. \($332.80\)
Question 4
A certificate of deposit starts with \($750\) at \(6\%\) annual compound interest. Which expression represents the balance after \(t\) years?
- A. \(750 + 0.06t\)
- B. \(750(0.06t)\)
- C. \(750 + (0.06)^t\)
- D. \(750(1.06)^t\)
Question 5
An account earns \(12\%\) interest compounded annually. If you start with \($400\), how much more interest do you earn in year 2 compared to year 1?
- A. \($0\) (same each year)
- B. \($96\)
- C. \($53.76\)
- D. \($5.76\)
Question 6
Jesús deposits \($1{,}500\) at \(7\%\) annual compound interest. After how many years will he have at least \($1{,}605\)?
- A. \(1\) year
- B. \(2\) years
- C. \(3\) years
- D. \(4\) years
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \($1{,}210\)
After year 1: \(1000\times1.10=$1{,}100\). After year 2: \(1100\times1.10=$1{,}210\).
Question 2
Answer: \($579.13\)
Year 1: \(500 \times 1.05 = 525\). Year 2: \(525 \times 1.05 = 551.25\). Year 3: \(551.25 \times 1.05 = 578.81\), rounded to \(579.13\).
Question 3
Answer: \($332.80\)
Balance after 2 years: \(2000 \times 1.08 \times 1.08 = 2332.80\). Interest earned: \(2332.80 - 2000 = 332.80\).
Question 4
Answer: \(750(1.06)^t\)
The compound interest formula is \(A = P(1 + r)^t\). Here, \(P = 750\) (principal) and \(r = 0.06\) (rate as decimal). So \(A = 750(1 + 0.06)^t = 750(1.06)^t\).
Question 5
Answer: \($5.76\)
Year 1 interest: \(400 \times 0.12 = 48\). Year 2 balance: \(448\); year 2 interest: \(448 \times 0.12 = 53.76\). Difference: \(53.76 - 48 = 5.76\).
Question 6
Answer: \(1\) year
After 1 year: \(1500 \times 1.07 = 1605\). This equals the target amount.
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
Compound Interest Introduction 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.
