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:
-
Calculate the loan amount you can afford:
- Use the monthly mortgage payment formula to determine the loan amount :
- Where:
- (monthly payment)
- (monthly interest rate)
- (total payments over 30 years)
-
Calculate the maximum loan amount:
- Rearrange the formula to solve for :
-
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:
- How would a lower interest rate affect the maximum home price you can afford?
- What would the maximum home price be if you increased your down payment to 30%?
- How much would you save in interest if you chose a 15-year mortgage instead?
- What happens if your monthly budget increases by $100? How does it affect the maximum price?
- 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
-
Suitable Grade Level
Adult Learners
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