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Grade 7 · lesson 4 of 4

Separate Interest from a Total Balance

Simple interest is proportional to principal, time, and rate.

About 20 minutes, plus any extended practice

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Supplied materials

  • Paper or a browser scratch area; a calculator is optional unless rounding is requested.
  • Supplied teaching case: A fictional simple-interest model uses principal $200, annual rate 4%, and 3 years. What interest alone accrues? Candidate answers: (A) 224 USD (B) 24 USD (C) 24.9728 USD (D) 8 USD.
  • Independent check inputs: A fictional simple-interest model uses principal $300, annual rate 4%, and 4 years. What interest alone accrues? Candidate answers: (A) 12 USD (B) 348 USD (C) 48 USD (D) 50.9576 USD.

Learn the idea

A percent is a ratio per hundred, but its base quantity matters. Successive percent operations act on successive amounts; reverse problems recover the original base rather than simply adding back a percentage. Simple interest is proportional to principal, time, and rate. Its formula I=Prt assumes the same original principal is used throughout; interest is not added to the interest base.

Here is the method on the supplied teaching case. Use I=Prt=200×0.04×3=24.0. Simple interest uses the original principal every year. This question asks for interest, not principal plus interest.

Convert the annual percent to a decimal and use years for time. This is a simplified educational model, not a financial offer; interest alone excludes the returned principal.

  1. Write or sketch the supplied teaching case, labeling its quantities and restrictions.
  2. Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
  3. Solve the independent check with its changed inputs before revealing feedback.
  4. Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.
Worked example

See the method in action

Teaching case: A fictional simple-interest model uses principal $200, annual rate 4%, and 3 years. What interest alone accrues? Candidate answers: (A) 224 USD (B) 24 USD (C) 24.9728 USD (D) 8 USD. Solution: Use I=Prt=200×0.04×3=24.0. Simple interest uses the original principal every year. This question asks for interest, not principal plus interest. The final answer is 24 USD. Convert the annual percent to a decimal and use years for time. This is a simplified educational model, not a financial offer; interest alone excludes the returned principal.

Your turn

Check your reasoning

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Helpful tips
  • Simple interest is proportional to principal, time, and rate.
  • Convert the annual percent to a decimal and use years for time.
A fictional simple-interest model uses principal $300, annual rate 4%, and 4 years. What interest alone accrues?

Feedback appears here after you check. This is practice, not a graded school assessment.

See the answer and explanation

48 USD

Use I=Prt=300×0.04×4=48.0. Simple interest uses the original principal every year. This question asks for interest, not principal plus interest.

Take it further

Changed-input task: A fictional simple-interest model uses principal $900, annual rate 4%, and 10 years. What interest alone accrues? Candidate answers: (A) 1260 USD (B) 36 USD (C) 360 USD (D) 432.2199 USD. Show the mathematical reason, not only the selected answer. Expected result: 360 USD. Use I=Prt=900×0.04×10=360.0. Simple interest uses the original principal every year. This question asks for interest, not principal plus interest.

Nothing here is saved to an account or sent to a teacher. The answer download includes your current choice and any checked feedback. It does not include choices from the separate More practice section. Download that section separately.

More practice: try new cases

Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.

More practice: try new cases
1. A fictional simple-interest model uses principal $400, annual rate 4%, and 5 years. What interest alone accrues?
Need a hint?
  • Simple interest is proportional to principal, time, and rate.
  • Convert the annual percent to a decimal and use years for time.
2. A fictional simple-interest model uses principal $500, annual rate 4%, and 6 years. What interest alone accrues?
Need a hint?
  • Simple interest is proportional to principal, time, and rate.
  • Convert the annual percent to a decimal and use years for time.
3. A fictional simple-interest model uses principal $600, annual rate 4%, and 7 years. What interest alone accrues?
Need a hint?
  • Simple interest is proportional to principal, time, and rate.
  • Convert the annual percent to a decimal and use years for time.

Your choices are temporary. Feedback appears after you check all the answers.

Nothing here is saved to an account or sent to a teacher. Keep your own notes or download them before leaving. The score describes these questions; it does not certify subject mastery.

Check the subject sources

These LifeStarter passages, scenarios and exercises are authored for this Academy with AI assistance and review. External resources keep their publishers’ terms. A grade label suggests a starting level; it does not establish alignment with your school’s complete requirements.