Math Problem Statement

After looking at your budget, you have decided that you can afford a monthly mortgage payment of $1,247.  What is the maximum price you can spend on a house if you plan to put 20% down and use a 30-year fixed-rate mortgage with an interest rate of 3.97%?

Answer should be formatted as a dollar amount rounded to the nearest cent.  

Solution

To find the maximum price you can spend on a house based on your budgeted monthly payment of $1,247, a 20% down payment, and a 30-year fixed-rate mortgage at 3.97%, we'll follow these steps:

  1. Calculate the loan amount you can afford:

    • Use the monthly mortgage payment formula to determine the loan amount PP:
    M=Pr(1+r)n(1+r)n1M = P \frac{r(1+r)^n}{(1+r)^n - 1}
    • Where:
      • M=1247M = 1247 (monthly payment)
      • r=3.97%12r = \frac{3.97\%}{12} (monthly interest rate)
      • n=30×12n = 30 \times 12 (total payments over 30 years)
  2. Calculate the maximum loan amount:

    • Rearrange the formula to solve for PP:
    P=M(1+r)n1r(1+r)nP = M \frac{(1+r)^n - 1}{r(1+r)^n}
  3. Calculate the maximum home price:

    • Since the loan amount represents 80% of the home's value (after a 20% down payment), divide the loan amount by 0.80 to find the maximum home price.

Let's calculate the maximum home price step-by-step.The maximum price you can spend on a house, given your budget and the specified mortgage terms, is $327,683.70.

Would you like more details or have any questions? Here are some related questions:

  1. How would a lower interest rate affect the maximum home price you can afford?
  2. What would the maximum home price be if you increased your down payment to 30%?
  3. How much would you save in interest if you chose a 15-year mortgage instead?
  4. What happens if your monthly budget increases by $100? How does it affect the maximum price?
  5. How do property taxes and insurance affect your overall budget for home buying?

Tip: Increasing your down payment can significantly increase the maximum home price you can afford while keeping the monthly payment the same!

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Math Problem Analysis

Mathematical Concepts

Finance
Mortgage Calculations

Formulas

Monthly mortgage payment formula
Loan amount calculation formula

Theorems

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Suitable Grade Level

Adult Learners