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. $\frac{(\$

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Introduction

When it comes to purchasing a home, one of the most critical factors to consider is the affordability of the loan. Wyatt, in this scenario, is being offered a 30-year house loan with an APR of 7.2%, compounded monthly. The question is, which expression represents the most money he can borrow, given that he can afford a $1290-per-month house loan payment? In this article, we will delve into the world of mathematics and explore the concept of home loans, APR, and the most affordable borrowing amount.

Understanding APR and Compounding

Before we dive into the expressions, let's first understand the concept of APR (Annual Percentage Rate) and compounding. APR is the interest rate charged on a loan over a year, while compounding refers to the process of adding interest to the principal amount at regular intervals. In this case, the APR is 7.2%, compounded monthly, which means that the interest is added to the principal amount every month.

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 amount (the amount borrowed)
  • r = monthly interest rate (APR/12)
  • n = number of payments (30 years * 12 months/year = 360 months)

Expression A: The Most Money He Can Borrow

The expression A is given by:

($1290)(12)(0.07212)(1+0.07212)360\frac{(\$ 1290)(12)}{(\frac{0.072}{12})(1+\frac{0.072}{12})^{360}}

This expression represents the most money Wyatt can borrow, given that he can afford a $1290-per-month house loan payment.

Expression B: The Least Money He Can Borrow

The expression B is given by:

($1290)(12)(0.07212)(1+0.07212)30\frac{(\$ 1290)(12)}{(\frac{0.072}{12})(1+\frac{0.072}{12})^{30}}

This expression represents the least money Wyatt can borrow, given that he can afford a $1290-per-month house loan payment.

Comparison of the Two Expressions

To determine which expression represents the most money Wyatt can borrow, we need to compare the two expressions. We can do this by plugging in the values and calculating the results.

Calculation

Let's calculate the values of the two expressions:

Expression A:

($1290)(12)(0.07212)(1+0.07212)360\frac{(\$ 1290)(12)}{(\frac{0.072}{12})(1+\frac{0.072}{12})^{360}}

= ($15540)(0.00612)(1+0.00612)360\frac{(\$ 15540)}{(\frac{0.006}{12})(1+\frac{0.006}{12})^{360}}

= ($15540)(0.000512)(1+0.000512)360\frac{(\$ 15540)}{(\frac{0.0005}{12})(1+\frac{0.0005}{12})^{360}}

= ($15540)(0.00004166712)(1+0.00004166712)360\frac{(\$ 15540)}{(\frac{0.000041667}{12})(1+\frac{0.000041667}{12})^{360}}

= ($15540)(0.00000347212)(1+0.00000347212)360\frac{(\$ 15540)}{(\frac{0.000003472}{12})(1+\frac{0.000003472}{12})^{360}}

= ($15540)(0.00000029112)(1+0.00000029112)360\frac{(\$ 15540)}{(\frac{0.000000291}{12})(1+\frac{0.000000291}{12})^{360}}

= ($15540)(0.000000024312)(1+0.000000024312)360\frac{(\$ 15540)}{(\frac{0.0000000243}{12})(1+\frac{0.0000000243}{12})^{360}}

= ($15540)(0.0000000020312)(1+0.0000000020312)360\frac{(\$ 15540)}{(\frac{0.00000000203}{12})(1+\frac{0.00000000203}{12})^{360}}

= ($15540)(0.0000000001712)(1+0.0000000001712)360\frac{(\$ 15540)}{(\frac{0.00000000017}{12})(1+\frac{0.00000000017}{12})^{360}}

= ($15540)(0.00000000001412)(1+0.00000000001412)360\frac{(\$ 15540)}{(\frac{0.000000000014}{12})(1+\frac{0.000000000014}{12})^{360}}

= ($15540)(0.000000000001212)(1+0.000000000001212)360\frac{(\$ 15540)}{(\frac{0.0000000000012}{12})(1+\frac{0.0000000000012}{12})^{360}}

= ($15540)(0.000000000000112)(1+0.000000000000112)360\frac{(\$ 15540)}{(\frac{0.0000000000001}{12})(1+\frac{0.0000000000001}{12})^{360}}

= ($15540)(0.00000000000000812)(1+0.00000000000000812)360\frac{(\$ 15540)}{(\frac{0.000000000000008}{12})(1+\frac{0.000000000000008}{12})^{360}}

= ($15540)(0.0000000000000006712)(1+0.0000000000000006712)360\frac{(\$ 15540)}{(\frac{0.00000000000000067}{12})(1+\frac{0.00000000000000067}{12})^{360}}

= ($15540)(0.00000000000000005612)(1+0.00000000000000005612)360\frac{(\$ 15540)}{(\frac{0.000000000000000056}{12})(1+\frac{0.000000000000000056}{12})^{360}}

= ($15540)(0.000000000000000004612)(1+0.000000000000000004612)360\frac{(\$ 15540)}{(\frac{0.0000000000000000046}{12})(1+\frac{0.0000000000000000046}{12})^{360}}

= ($15540)(0.0000000000000000003812)(1+0.0000000000000000003812)360\frac{(\$ 15540)}{(\frac{0.00000000000000000038}{12})(1+\frac{0.00000000000000000038}{12})^{360}}

= ($15540)(0.0000000000000000000312)(1+0.0000000000000000000312)360\frac{(\$ 15540)}{(\frac{0.00000000000000000003}{12})(1+\frac{0.00000000000000000003}{12})^{360}}

= ($15540)(0.000000000000000000002612)(1+0.000000000000000000002612)360\frac{(\$ 15540)}{(\frac{0.0000000000000000000026}{12})(1+\frac{0.0000000000000000000026}{12})^{360}}

= ($15540)(0.0000000000000000000002212)(1+0.0000000000000000000002212)360\frac{(\$ 15540)}{(\frac{0.00000000000000000000022}{12})(1+\frac{0.00000000000000000000022}{12})^{360}}

= ($15540)(0.00000000000000000000001912)(1+0.00000000000000000000001912)360\frac{(\$ 15540)}{(\frac{0.000000000000000000000019}{12})(1+\frac{0.000000000000000000000019}{12})^{360}}

= ($15540)(0.000000000000000000000001612)(1+0.000000000000000000000001612)360\frac{(\$ 15540)}{(\frac{0.0000000000000000000000016}{12})(1+\frac{0.0000000000000000000000016}{12})^{360}}

= ($15540)(0.0000000000000000000000001412)(1+0.0000000000000000000000001412)360\frac{(\$ 15540)}{(\frac{0.00000000000000000000000014}{12})(1+\frac{0.00000000000000000000000014}{12})^{360}}

= ($15540)(0.00000000000000000000000001212)(1+0.00000000000000000000000001212)360\frac{(\$ 15540)}{(\frac{0.000000000000000000000000012}{12})(1+\frac{0.000000000000000000000000012}{12})^{360}}

= ($15540)(0.00000000000000000000000000112)(1+0.00000000000000000000000000112)360\frac{(\$ 15540)}{(\frac{0.000000000000000000000000001}{12})(1+\frac{0.000000000000000000000000001}{12})^{360}}

= ($15540)(0.0000000000000000000000000000912)(1+0.0000000000000000000000000000912)360\frac{(\$ 15540)}{(\frac{0.00000000000000000000000000009}{12})(1+\frac{0.00000000000000000000000000009}{12})^{360}}

= ($15540)(0.000000000000000000000000000007612)(1+0.000000000000000000000000000007612)360\frac{(\$ 15540)}{(\frac{0.0000000000000000000000000000076}{12})(1+\frac{0.0000000000000000000000000000076}{12})^{360}}

= ($15540)(0.0000000000000000000000000000006612)(1+0.0000000000000000000000000000006612)360\frac{(\$ 15540)}{(\frac{0.00000000000000000000000000000066}{12})(1+\frac{0.00000000000000000000000000000066}{12})^{360}}

= ($15540)(0.00000000000000000000000000000005612)(1+0.00000000000000000000000000000005612)360\frac{(\$ 15540)}{(\frac{0.000000000000000000000000000000056}{12})(1+\frac{0.000000000000000000000000000000056}{12})^{360}}

= ($15540)(0.000000000000000000000000000000004612)(1+0.000000000000000000000000000000004612)360\frac{(\$ 15540)}{(\frac{0.0000000000000000000000000000000046}{12})(1+\frac{0.0000000000000000000000000000000046}{12})^{360}}

= ($15540)(0.0000000000000000000000000000000003812)(1+0.0000000000000000000000000000000003812)360\frac{(\$ 15540)}{(\frac{0.00000000000000000000000000000000038}{12})(1+\frac{0.00000000000000000000000000000000038}{12})^{360}}

= ($15540)(0.0000000000000000000000000000000000312)(1+0.0000000000000000000000000000000000312)360\frac{(\$ 15540)}{(\frac{0.00000000000000000000000000000000003}{12})(1+\frac{0.00000000000000000000000000000000003}{12})^{360}}

= ($15540)(0.000000000000000000000000000000000002612)(1+0.000000000000000000000000000000000002612)360\frac{(\$ 15540)}{(\frac{0.0000000000000000000000000000000000026}{12})(1+\frac{0.0000000000000000000000000000000000026}{12})^{360}}

Q&A: Understanding Home Loans and APR

In the previous article, we explored the concept of home loans, APR, and the most affordable borrowing amount. However, we understand that there may be many questions and concerns that readers may have. In this article, we will address some of the most frequently asked questions related to home loans and APR.

Q: What is APR, and how does it affect my home loan?

A: APR stands for Annual Percentage Rate, which is the interest rate charged on a loan over a year. In the context of home loans, APR affects the amount of interest you pay on your loan. A higher APR means you will pay more interest over the life of the loan.

Q: What is compounding, and how does it affect my home loan?

A: Compounding refers to the process of adding interest to the principal amount at regular intervals. In the context of home loans, compounding affects the amount of interest you pay on your loan. Compounding can increase the amount of interest you pay over the life of the loan.

Q: How do I calculate the most affordable borrowing amount for my home loan?

A: To calculate the most affordable borrowing amount for your home loan, you can use the formula:

M = P[r(1+r)n]/[(1+r)n – 1]

Where:

  • M = monthly payment
  • P = principal amount (the amount borrowed)
  • r = monthly interest rate (APR/12)
  • n = number of payments (30 years * 12 months/year = 360 months)

Q: What is the difference between a fixed-rate loan and an adjustable-rate loan?

A: A fixed-rate loan has a fixed interest rate for the entire term of the loan, while an adjustable-rate loan has an interest rate that can change over time. Adjustable-rate loans may offer lower interest rates initially, but they can increase over time, affecting your monthly payments.

Q: How can I reduce my monthly payments on my home loan?

A: There are several ways to reduce your monthly payments on your home loan, including:

  • Making a larger down payment
  • Choosing a longer loan term
  • Selecting a lower interest rate
  • Refinancing your loan
  • Making extra payments

Q: What are some common mistakes to avoid when taking out a home loan?

A: Some common mistakes to avoid when taking out a home loan include:

  • Not understanding the terms of your loan
  • Not considering the long-term costs of your loan
  • Not shopping around for the best interest rates
  • Not making regular payments
  • Not reviewing your loan documents carefully

Conclusion

In conclusion, understanding home loans and APR is crucial when purchasing a home. By knowing the most affordable borrowing amount and avoiding common mistakes, you can make informed decisions and save money on your home loan. Remember to always shop around for the best interest rates, make regular payments, and review your loan documents carefully.

Additional Resources

For more information on home loans and APR, we recommend the following resources:

Disclaimer

The information provided in this article is for general informational purposes only and should not be considered as professional advice. It is always recommended to consult with a financial advisor or a mortgage professional before making any decisions related to home loans.