Math Problem Statement
Karen and Wayne need to buy a refrigerator because theirs just broke. Unfortunately, their savings account is depleted, and they will need to borrow money in order to buy a new one. Sears offers them an installment loan at 12% (add-on rate). If the refrigerator at Sears costs $1,568 plus 5% sales tax, and Karen and Wayne plan to pay for the refrigerator for 3 years, what is the monthly payment? (Round your answer to the nearest cent.)
Solution
To calculate the monthly payment for Karen and Wayne's refrigerator loan, we will follow these steps:
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Calculate the total cost of the refrigerator including sales tax:
- Cost of the refrigerator: $1,568
- Sales tax: 5% of $1,568
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Calculate the total interest on the loan:
- The add-on rate is 12%, which means the interest is calculated on the total loan amount for the full term.
- Total amount borrowed: $1,646.40
- Total interest for 3 years:
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Calculate the total amount to be repaid:
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Calculate the monthly payment:
- Total payment period: 3 years = 36 months
Thus, the monthly payment for Karen and Wayne will be approximately $62.75.
If you have any questions or would like more details, feel free to ask! Here are some related questions to consider:
- What would the total cost be if the refrigerator price increased by 10%?
- How would the monthly payment change if they extended the loan term to 4 years?
- What are the implications of using a credit card instead of a loan for this purchase?
- How much total interest would they pay if the loan had an interest rate of 10% instead of 12%?
- What are some alternatives to financing a refrigerator purchase?
Tip: Always consider the total cost of financing (including interest) when making large purchases on credit.
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Math Problem Analysis
Mathematical Concepts
Interest Calculation
Installment Loan
Percentage
Monthly Payment Calculation
Formulas
Total cost = Initial price + (Sales tax rate * Initial price)
Total interest = Principal * Add-on rate * Loan term (years)
Total repayment = Total cost + Total interest
Monthly payment = Total repayment / (Loan term in years * 12)
Theorems
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Suitable Grade Level
Grades 10-12
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