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Solving a Word Problem for the Rate of Simple Interest on Jim's Loan
Apply the problem-solving strategy to find the rate of simple interest given the principal, interest earned, and time.
Problem: Jim lent his sister to help her buy a house. In years, she paid him the , plus interest. What was the rate of simple interest?
- Read the problem carefully.
- Identify what to find: the rate of simple interest.
- Name the unknown: Let = rate of interest.
- Translate into an equation using the simple interest formula . Given , , and :
- Solve the equation: Multiply and : Divide both sides by : Change the decimal to percent form:
- Check the result:
- Answer: The rate of interest was .
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In the scenario where Jim lent his sister for years and received in simple interest, match each component of the simple interest formula () with its corresponding value or description from the problem.
Jim lent his sister 5,000 dollars to help her buy a house. In 3 years, she paid him back the principal plus 900 dollars in interest. To calculate the annual simple interest rate () Jim charged using the formula , place the following steps of the problem-solving strategy in the correct order.
Jim lent his sister 5,000 dollars to help her buy a house. In 3 years, she paid him the 5,000 dollars plus 900 dollars in simple interest. Based on this scenario, what was the annual rate of simple interest () that Jim charged?
In the simple interest formula , the principal () for Jim's loan represents the total amount his sister returned to him (the initial loan plus the interest), which equals .
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