Wyatt Can Afford A $\$1290$-per-month House Loan Payment. If He Is Being Offered A 30-year House Loan With An APR Of $7.2\%$, Compounded Monthly, Which Of These Expressions Represents The Most Money He Can Borrow? A.

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Wyatt's Home Loan Options: Understanding the Mathematics Behind the Mortgage

When it comes to purchasing a home, one of the most critical factors to consider is the affordability of the mortgage. In this article, we will delve into the world of mathematics and explore the concept of home loans, specifically focusing on Wyatt's situation. With a monthly payment of $1290, a 30-year loan term, and an APR of 7.2% compounded monthly, we will examine which expression represents the most money Wyatt can borrow.

Understanding the Key Components

Before we dive into the calculations, let's break down the key components of Wyatt's home loan:

  • Monthly payment: $1290
  • Loan term: 30 years
  • APR: 7.2% compounded monthly
  • Interest rate: 7.2%/year = 0.006 per month (since it's compounded monthly)

The Formula for Monthly Payments

The formula for monthly payments on a fixed-rate loan is given by:

M = P[r(1+r)n]/[(1+r)n – 1]

Where:

  • M = monthly payment
  • P = principal loan amount (the amount Wyatt can borrow)
  • r = monthly interest rate (0.006 in this case)
  • n = number of payments (30 years * 12 months/year = 360 months)

Expression A: The Most Money Wyatt Can Borrow

To find the expression that represents the most money Wyatt can borrow, we need to rearrange the formula to solve for P. This gives us:

P = M[(1+r)^n – 1]/[r(1+r)^n]

Substituting the values we know, we get:

P = 1290[(1+0.006)^360 – 1]/[0.006(1+0.006)^360]

Calculating the Principal Loan Amount

Using a calculator or software to compute the expression, we get:

P ≈ $173,919.19

This is the most money Wyatt can borrow, given his monthly payment of $1290, a 30-year loan term, and an APR of 7.2% compounded monthly.

Conclusion

In conclusion, when it comes to determining the most money Wyatt can borrow, we need to consider the key components of his home loan, including the monthly payment, loan term, APR, and interest rate. By using the formula for monthly payments and rearranging it to solve for the principal loan amount, we can determine the maximum amount Wyatt can borrow. In this case, the expression P = 1290[(1+0.006)^360 – 1]/[0.006(1+0.006)^360] represents the most money Wyatt can borrow, which is approximately $173,919.19.

Additional Considerations

While this calculation provides a good estimate of the most money Wyatt can borrow, there are other factors to consider when purchasing a home. These include:

  • Closing costs: These are fees associated with the home buying process, such as title insurance, appraisal fees, and loan origination fees.
  • Property taxes: These are taxes levied on the property owner, which can vary depending on the location and value of the property.
  • Insurance: Homeowners insurance is typically required to protect against damage or loss to the property.
  • Maintenance and repairs: Homeowners are responsible for maintaining and repairing the property, which can be a significant expense.

Real-World Applications

Understanding the mathematics behind home loans can have a significant impact on one's financial situation. By considering the key components of a home loan and using the formula for monthly payments, individuals can make informed decisions about their borrowing capacity. This knowledge can be applied in various real-world scenarios, such as:

  • Home buying: When purchasing a home, individuals need to consider their borrowing capacity and ensure that they can afford the monthly payments.
  • Refinancing: When refinancing a home loan, individuals need to consider the new interest rate, loan term, and monthly payments to determine if it is beneficial to refinance.
  • Investing: Understanding the mathematics behind home loans can also be applied to investing in real estate, where individuals can use the formula for monthly payments to determine the potential return on investment.

Conclusion

In conclusion, the mathematics behind home loans is complex and requires careful consideration of various factors. By understanding the key components of a home loan and using the formula for monthly payments, individuals can make informed decisions about their borrowing capacity. In this article, we have explored the concept of home loans, specifically focusing on Wyatt's situation, and determined that the expression P = 1290[(1+0.006)^360 – 1]/[0.006(1+0.006)^360] represents the most money he can borrow, which is approximately $173,919.19.