Liza Is Buying A Home For $213,575. She Is Making A 19% Down Payment And financing The Rest With A 25-year Loan At 4.00% Interest. What Will Her Total Payment for The Home Be?

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Understanding the Problem

Liza is buying a home for $213,575 and making a 19% down payment. The remaining amount will be financed with a 25-year loan at 4.00% interest. To calculate the total payment for the home, we need to determine the amount of the down payment, the amount financed, and the monthly payment.

Calculating the Down Payment

The down payment is 19% of the purchase price of the home.

Down payment = 19% of $213,575
Down payment = 0.19 x $213,575
Down payment = $40,478.25

Calculating the Amount Financed

The amount financed is the purchase price of the home minus the down payment.

Amount financed = Purchase price - Down payment
Amount financed = $213,575 - $40,478.25
Amount financed = $173,096.75

Calculating the Monthly Payment

To calculate the monthly payment, we can use the formula for monthly payments on a fixed-rate loan:

M = P[r(1+r)n]/[(1+r)n – 1]

Where:

  • M = monthly payment
  • P = principal loan amount (amount financed)
  • r = monthly interest rate (annual interest rate / 12)
  • n = number of payments (25 years * 12 months/year)
Monthly interest rate = 4.00%/year / 12 months/year
Monthly interest rate = 0.003333

Number of payments = 25 years * 12 months/year
Number of payments = 300 months


Monthly payment = $173,096.75[0.003333(1+0.003333)300]/[(1+0.003333)300 – 1]
Monthly payment ≈ $1,044.19

Calculating the Total Payment

The total payment for the home is the monthly payment multiplied by the number of payments.

Total payment = Monthly payment \* Number of payments
Total payment = $1,044.19 \* 300
Total payment ≈ $313,257.00

Conclusion

In this example, Liza's total payment for the home will be approximately $313,257.00. This includes the down payment of $40,478.25, the amount financed of $173,096.75, and the monthly payments of $1,044.19 for 300 months.

Key Takeaways

  • The down payment is 19% of the purchase price of the home.
  • The amount financed is the purchase price of the home minus the down payment.
  • The monthly payment can be calculated using the formula for monthly payments on a fixed-rate loan.
  • The total payment for the home is the monthly payment multiplied by the number of payments.

Real-World Applications

This problem can be applied to real-world situations where individuals are purchasing a home and need to calculate the total payment. It can also be used to compare different loan options and interest rates.

Mathematical Concepts

This problem involves the following mathematical concepts:

  • Percentages: calculating the down payment as a percentage of the purchase price
  • Algebra: using the formula for monthly payments on a fixed-rate loan
  • Exponents: calculating the monthly interest rate and the number of payments
  • Multiplication: calculating the total payment by multiplying the monthly payment by the number of payments
    Frequently Asked Questions (FAQs) about Calculating Total Payment for a Home Purchase =====================================================================================

Q: What is the formula for calculating the total payment for a home purchase?

A: The formula for calculating the total payment for a home purchase involves several steps:

  1. Calculate the down payment as a percentage of the purchase price.
  2. Calculate the amount financed by subtracting the down payment from the purchase price.
  3. Use the formula for monthly payments on a fixed-rate loan to calculate the monthly payment.
  4. Multiply the monthly payment by the number of payments to calculate the total payment.

Q: What is the formula for monthly payments on a fixed-rate loan?

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

M = P[r(1+r)n]/[(1+r)n – 1]

Where:

  • M = monthly payment
  • P = principal loan amount (amount financed)
  • r = monthly interest rate (annual interest rate / 12)
  • n = number of payments (number of years * 12 months/year)

Q: How do I calculate the monthly interest rate?

A: To calculate the monthly interest rate, divide the annual interest rate by 12.

Example: If the annual interest rate is 4.00%, the monthly interest rate would be:

Monthly interest rate = 4.00%/year / 12 months/year Monthly interest rate = 0.003333

Q: How do I calculate the number of payments?

A: To calculate the number of payments, multiply the number of years by 12.

Example: If the loan is for 25 years, the number of payments would be:

Number of payments = 25 years * 12 months/year Number of payments = 300 months

Q: What is the difference between a down payment and an earnest money deposit?

A: A down payment is a percentage of the purchase price that is paid at the time of closing, while an earnest money deposit is a deposit made by the buyer to demonstrate their commitment to purchasing the property. The earnest money deposit is typically refundable if the buyer is unable to secure financing or if the sale falls through.

Q: Can I use a mortgage calculator to calculate the total payment for a home purchase?

A: Yes, you can use a mortgage calculator to calculate the total payment for a home purchase. However, be sure to enter the correct information, including the purchase price, down payment, interest rate, and loan term.

Q: What are some common mistakes to avoid when calculating the total payment for a home purchase?

A: Some common mistakes to avoid when calculating the total payment for a home purchase include:

  • Failing to account for closing costs and other fees associated with the loan
  • Using an incorrect interest rate or loan term
  • Failing to consider the impact of taxes and insurance on the monthly payment
  • Not taking into account any prepayment penalties or fees associated with the loan

Q: Can I refinance my mortgage to lower my monthly payment?

A: Yes, you can refinance your mortgage to lower your monthly payment. However, be sure to consider the costs associated with refinancing, including closing costs and any fees associated with the new loan. Additionally, be sure to review your credit report and credit score to ensure that you are eligible for the best interest rates and terms.

Q: What are some tips for negotiating a lower interest rate on a mortgage?

A: Some tips for negotiating a lower interest rate on a mortgage include:

  • Shopping around and comparing rates from different lenders
  • Considering a longer loan term to lower the monthly payment
  • Making a larger down payment to reduce the amount financed
  • Negotiating with the lender to see if they can offer a better rate or terms
  • Considering a government-backed loan, such as an FHA or VA loan, which may offer more favorable terms.