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.)

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

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

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:

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

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

4. **Calculate the monthly payment**:
   - Total payment period: 3 years = 36 months

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

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.

Learn how to calculate the monthly payment for a $1,568 refrigerator purchased with a 3-year installment loan at a 12% add-on rate. This problem includes interest calculation, percentage-based tax, and monthly payment determination. Perfect for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation