Math Problem Statement

Kari is purchasing a home for $260,000. The down payment is 25% and the balance will be financed with a 15-year mortgage at 8% and 3 discount points. Kari made a deposit of $20,000 (applied to the down payment) when the sales contract was signed. Kari also has these expenses: credit report, $90; appraisal fee, $110; title insurance premium, 1% of amount financed; title search, $300; and attorney's fees, $500. Find the closing costs (in $).

Solution

To solve this problem, we need to determine Kari's total closing costs based on the given information.

Step-by-Step Calculation

  1. Calculate the Down Payment: Down Payment=25%×260,000=0.25×260,000=65,000\text{Down Payment} = 25\% \times 260,000 = 0.25 \times 260,000 = 65,000

  2. Calculate the Amount Financed: Amount Financed=260,00065,000=195,000\text{Amount Financed} = 260,000 - 65,000 = 195,000

  3. Discount Points Cost: The cost of each discount point is 1% of the amount financed. Since Kari is paying for 3 discount points: Discount Points Cost=3%×195,000=0.03×195,000=5,850\text{Discount Points Cost} = 3\% \times 195,000 = 0.03 \times 195,000 = 5,850

  4. Title Insurance Premium: The title insurance premium is also calculated as 1% of the amount financed: Title Insurance Premium=1%×195,000=0.01×195,000=1,950\text{Title Insurance Premium} = 1\% \times 195,000 = 0.01 \times 195,000 = 1,950

  5. Other Closing Costs: The additional closing costs are given directly:

    • Credit Report: $90
    • Appraisal Fee: $110
    • Title Search: $300
    • Attorney’s Fees: $500
  6. Total Closing Costs Calculation: Add all the individual costs together: Total Closing Costs=5,850+1,950+90+110+300+500=8,800\text{Total Closing Costs} = 5,850 + 1,950 + 90 + 110 + 300 + 500 = 8,800

Answer

Kari's total closing costs are $8,800.


Would you like further explanation or have any questions about this solution?


Here are some related questions to explore:

  1. How would the closing costs change if the discount points were reduced to 2 points?
  2. What would the amount financed be if Kari increased her down payment to 30%?
  3. How would a 10% mortgage interest rate impact the monthly payment compared to the current 8% rate?
  4. What additional costs might Kari face if she had to pay private mortgage insurance (PMI)?
  5. How would the closing costs change if the title insurance premium increased to 2%?

Tip: When calculating financial problems, always confirm that you are using the correct percentage rates for each component.

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Math Problem Analysis

Mathematical Concepts

Percentage
Basic Arithmetic
Financial Calculation

Formulas

Down Payment = Purchase Price * Down Payment Percentage
Amount Financed = Purchase Price - Down Payment
Discount Points Cost = Discount Points * Amount Financed
Title Insurance Premium = Title Insurance Percentage * Amount Financed
Total Closing Costs = Sum of All Costs

Theorems

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Suitable Grade Level

Grades 10-12