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:

  1. Calculate the total cost of the refrigerator including sales tax:

    • Cost of the refrigerator: $1,568
    • Sales tax: 5% of $1,568

    Sales tax=0.05×1568=78.40\text{Sales tax} = 0.05 \times 1568 = 78.40 Total cost=1568+78.40=1646.40\text{Total cost} = 1568 + 78.40 = 1646.40

  2. 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:

    Total interest=0.12×1646.40×3=0.12×4939.20=592.70\text{Total interest} = 0.12 \times 1646.40 \times 3 = 0.12 \times 4939.20 = 592.70

  3. Calculate the total amount to be repaid: Total repayment=Total cost+Total interest=1646.40+592.70=2239.10\text{Total repayment} = \text{Total cost} + \text{Total interest} = 1646.40 + 592.70 = 2239.10

  4. Calculate the monthly payment:

    • Total payment period: 3 years = 36 months

    Monthly payment=2239.103662.75\text{Monthly payment} = \frac{2239.10}{36} \approx 62.75

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:

  1. What would the total cost be if the refrigerator price increased by 10%?
  2. How would the monthly payment change if they extended the loan term to 4 years?
  3. What are the implications of using a credit card instead of a loan for this purchase?
  4. How much total interest would they pay if the loan had an interest rate of 10% instead of 12%?
  5. 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