Kylie Can Afford A $1310-per-month House Loan Payment. If She Is Being Offered A 25-year House Loan With An APR Of 8.4 % 8.4\% 8.4% , Compounded Monthly, Which Of These Expressions Represents The Most Money She Can Borrow?A.

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When it comes to determining the maximum amount that can be borrowed for a house loan, several factors come into play. In this scenario, we are given the monthly payment amount, the loan term, and the annual percentage rate (APR). Our goal is to find the expression that represents the most money Kylie can borrow.

Given Information

  • Monthly payment: $1310
  • Loan term: 25 years
  • APR: 8.4%
  • Compounding frequency: Monthly

Calculating the Maximum Borrowable Amount

To find the maximum amount that Kylie can borrow, we need to use the formula for calculating the present value of an annuity:

PV = PMT x [(1 - (1 + r)^(-n)) / r]

Where:

  • PV = Present Value (the maximum amount that can be borrowed)
  • PMT = Monthly payment
  • r = Monthly interest rate (APR / 12)
  • n = Number of payments (loan term in months)

Step 1: Convert the APR to a Monthly Interest Rate

First, we need to convert the APR to a monthly interest rate by dividing it by 12.

r = 8.4% / 12 = 0.007

Step 2: Calculate the Number of Payments

Next, we need to calculate the number of payments by multiplying the loan term in years by 12.

n = 25 years x 12 = 300 months

Step 3: Plug in the Values

Now that we have the monthly interest rate and the number of payments, we can plug in the values into the formula.

PV = 1310 x [(1 - (1 + 0.007)^(-300)) / 0.007]

Simplifying the Expression

To simplify the expression, we can use a calculator or a financial calculator to evaluate the expression.

PV ≈ 1310 x 173.19

PV ≈ $227,144.90

Conclusion

Based on the given information, the expression that represents the most money Kylie can borrow is:

PV = 1310 x [(1 - (1 + 0.007)^(-300)) / 0.007]

This expression takes into account the monthly payment, loan term, and APR to calculate the maximum amount that can be borrowed.

Additional Considerations

When calculating the maximum borrowable amount, it's essential to consider other factors such as:

  • Closing costs: These are fees associated with the loan process, such as origination fees, title insurance, and appraisal fees.
  • Property taxes: These are taxes levied on the property, which can vary depending on the location and type of property.
  • Insurance: This includes homeowners insurance, which protects the property against damage or loss.

By considering these factors, you can get a more accurate picture of the maximum amount that can be borrowed and the associated costs.

Real-World Applications

Calculating the maximum borrowable amount is a crucial step in the homebuying process. It helps borrowers determine how much they can afford to borrow and what their monthly payments will be. This information can be used to:

  • Determine the maximum loan amount: By calculating the maximum borrowable amount, borrowers can determine how much they can borrow and what their monthly payments will be.
  • Compare loan options: By comparing different loan options, borrowers can choose the one that best fits their needs and budget.
  • Create a budget: By knowing how much they can borrow and what their monthly payments will be, borrowers can create a budget that takes into account their income, expenses, and debt obligations.

Conclusion

In the previous article, we discussed how to calculate the maximum borrowable amount using the formula for calculating the present value of an annuity. However, we understand that you may have some questions about the process. Here are some frequently asked questions and their answers:

Q: What is the formula for calculating the present value of an annuity?

A: The formula for calculating the present value of an annuity is:

PV = PMT x [(1 - (1 + r)^(-n)) / r]

Where:

  • PV = Present Value (the maximum amount that can be borrowed)
  • PMT = Monthly payment
  • r = Monthly interest rate (APR / 12)
  • n = Number of payments (loan term in months)

Q: How do I calculate the monthly interest rate?

A: To calculate the monthly interest rate, you need to divide the APR by 12.

r = APR / 12

For example, if the APR is 8.4%, the monthly interest rate would be:

r = 8.4% / 12 = 0.007

Q: How do I calculate the number of payments?

A: To calculate the number of payments, you need to multiply the loan term in years by 12.

n = loan term in years x 12

For example, if the loan term is 25 years, the number of payments would be:

n = 25 years x 12 = 300 months

Q: What is the difference between the APR and the monthly interest rate?

A: The APR and the monthly interest rate are related but not the same thing. The APR is the annual interest rate, while the monthly interest rate is the interest rate divided by 12.

For example, if the APR is 8.4%, the monthly interest rate would be 0.007, which is the APR divided by 12.

Q: Can I use a financial calculator to calculate the present value of an annuity?

A: Yes, you can use a financial calculator to calculate the present value of an annuity. Many financial calculators have a built-in function for calculating the present value of an annuity.

Q: What are some common mistakes to avoid when calculating the present value of an annuity?

A: Some common mistakes to avoid when calculating the present value of an annuity include:

  • Forgetting to divide the APR by 12 to get the monthly interest rate
  • Forgetting to multiply the loan term in years by 12 to get the number of payments
  • Using the wrong formula or calculator function
  • Not considering other factors such as closing costs, property taxes, and insurance

Q: Can I use the present value of an annuity formula to calculate the maximum loan amount for a mortgage?

A: Yes, you can use the present value of an annuity formula to calculate the maximum loan amount for a mortgage. However, you need to consider other factors such as the loan term, APR, and monthly payment to get an accurate calculation.

Q: What are some real-world applications of the present value of an annuity formula?

A: The present value of an annuity formula has many real-world applications, including:

  • Calculating the maximum loan amount for a mortgage
  • Determining the monthly payment for a loan
  • Comparing different loan options
  • Creating a budget that takes into account income, expenses, and debt obligations

Conclusion

In conclusion, calculating the present value of an annuity is a complex process that involves several factors, including the monthly payment, loan term, and APR. By using the formula for calculating the present value of an annuity, you can determine the maximum amount that can be borrowed and what the monthly payments will be. We hope this article has helped you understand the process and provided you with some useful information.