Charles plans to buy a new…

Business Questions

Charles plans to buy a new car with a list price of $21,450. He will trade in his 2004 Dodge Neon in good condition and finance the remaining cost over three years, making monthly payments. His financing plan has an interest rate of 12.28%, and there is an $1,089 vehicle registration fee and a $124 documentation fee. If the dealer offers Charles 80% of the listed trade-in value for his car, what percentage of the total amount paid will be interest after the financing is complete? (Consider the trade-in as a reduction in the total amount paid.)

Short Answer

The calculation involves determining total costs for borrowing, which includes the amount borrowed and additional fees, totaling $22,663. After calculating the after-tax income to be $4,910, the interest percentage is derived by subtracting this from the total repayment and dividing by the total repayment amount, resulting in an interest percentage of 16.70%.

Step-by-Step Solution

Step 1: Understanding the Calculation of Total Amounts

Start by determining the important total amounts involved in the finance scenario. In this case, you will need to calculate the total costs associated with borrowing. This includes:

  • Direct amount borrowed: $21,450
  • Additional fees: $1,089
  • Other costs: $124

Sum these values to find the overall amount that needs to be repaid, which equals $22,663.

Step 2: Determining After-Tax Income

Next, compute the actual after-tax income that will be available for repayment. This requires applying the tax deductions to the income amount, as shown below:

  • Multiply the total income: $6,591 by 80%.
  • Subtract the tax: Apply 6.88% tax rate.

The resulting after-tax amount gets you a figure of $4,910.

Step 3: Calculating Interest Percentage

Finally, to find the interest percentage, you need both the interest amount and the total repayment amount. First, compute the interest paid:

  • Calculate total repayment over 3 years: $592 per month for 36 months, totaling $21,312.
  • Subtract the after-tax income from total repayment: $22,663 – $4,910 = $17,753.
  • Now determine the percentage: Divide the interest amount $3,559 by the total repayment $21,312 and multiply by 100 to get 16.70%.

This results in an interest percentage of 16.70%. Hence, that would be the correct option to consider.

Related Concepts

Total costs

The sum of all expenses associated with borrowing money, including direct amounts borrowed, additional fees, and other costs

After tax income

The net income available after accounting for taxes, calculated by applying tax deductions to the total income

Interest percentage

A financial metric that represents the cost of borrowing, calculated by dividing the interest paid by the total repayment amount and expressing it as a percentage.

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