mortgage Math

Chapter Eight: More Mortgage Math

Learning Objectives

• After completing this chapter, students will be able to:
  • Solve for monthly payments using a mortgage factor chart.
  • Solve for the cost of mortgage points and understand their significance.

Main Concepts

• There are two primary concepts to learn in this chapter:
  • The use of a mortgage factor chart.
  • The concept of points.

Mortgage Factor Chart

• The mortgage factor chart is a tool that helps calculate a borrower's monthly payment.
• Finding the mortgage factor:
  • Locate the appropriate interest rate in the chart.
  • Follow the row to find the column corresponding to the loan term (either fifteen or thirty years).
  • The resulting number is the mortgage factor, which represents the monthly principal and interest (P + I) payment for a $1,000 loan.
• Calculating the payment for a larger loan:
  • Formula:
  • ext{Monthly Payment} = ext{Mortgage Factor} imes rac{ ext{Loan Principal}}{1000}
  • For example:
  • Interest Rate: 5.5%
  • Term: 30 years
  • Mortgage Factor from chart: 5.68
  • Loan Amount: $250,000
  • Calculation:
    • $250 imes 5.68 = 1420$ monthly payment.

Comparing Monthly Payments of Different Loans

• Loan Number One:

  • Loan Amount: $200,000
  • Interest Rate: 5%
  • Term: 15 years
  • Mortgage Factor: 7.91
  • Monthly Payment Calculation:
  • $200 imes 7.91 = 1582$ monthly payment.

• Loan Number Two:

  • Loan Amount: $200,000
  • Interest Rate: 6.13%
  • Term: 30 years
  • Mortgage Factor: 6.08
  • Monthly Payment Calculation:
  • $200 imes 6.08 = 1216$ monthly payment.

• Comparison of Payments:

  • Loan number two's payment of $1,216 is $366 cheaper than loan number one's payment of $1,582.
  • Note: Loan number two has a thirty-year term while loan number one has a fifteen-year term, leading to higher total payments in the long run due to more payments made.

Understanding Points

• Definition: Points are fees paid by the borrower when they take out a loan. They include:
  • Discount Points: Fees paid upfront to lower the interest rate on a mortgage.
  • Origination Points: Fees charged by the lender for processing or originating the mortgage loan.

Discount Points

• What are discount points?:
  • Each point equals 1% of the loan principal.
  • Paying discount points allows borrowers to lower their rate by prepaying interest.
• Strategy:
  • The effectiveness of paying points can vary based on lender offers and the borrower's duration in the loan.
  • A typical reduction is 25 basis points (0.25%) for the first discount point purchased.
  • Additional points may not significantly reduce the rate, emphasizing the need to review lender details carefully.

Origination Points

• Definition:
  • Fees charged by a lender which may also be referred to as origination fees.
  • Origination points are calculated similarly:
  • 1 point = 1% of the loan value.
  • Occasionally expressed as a percentage different from points (e.g., 1.5% origination fee).

Point Math

• Key Takeaways:

  • Formula for Point Costs:
  • $ext{Loan Points} imes ext{Loan Principal} = ext{Total Cost of Points}$
  • Example Problem:
  • Angeline's $250,000 mortgage with 4 discount points:
    1. Convert points to percentage: 4 points = 4% of loan.
    2. Convert percentage to decimal: 4 ext{%} = 0.04.
    3. Multiply to find total cost:
    • $0.04 imes 250,000 = 10,000$.

• Finding Loan Principal from Points:

  • Formula:
  • ext{Total Cost of Points} igg / ext{Number of Points} = ext{Cost Per Point}
  • If LeAnna bought 5 discount points for $7,500:
    1. Find cost of one point: 7500 igg / 5 = 1500.
    2. Multiply cost per point by 100 for loan principal:
    • $1500 imes 100 = 150,000$ loan principal.

Total Cash Required to Close

• Example: Liam's loan situation
  • Loan Amount: $170,000
  • Points: Two discount points and one origination point
  • Down Payment: 10%

Calculating Total Cash Needed

1. Finding total points cost:

   • Calculate the total cost of points (3% of $170,000):
     • $170,000 imes 0.03 = 5100$.

2. Finding purchase price:

   • Recognize $170,000 is 90% of the purchase price:
     • 170,000 igg / 0.9 = 188,888.89 purchase price.

3. Calculating down payment:

   • Down payment = Purchase Price - Loan Amount:
     • $188,888.89 - 170,000 = 18,888.89$ (down payment).

4. Total cost to close:

   • Total Amount = Down Payment + Points:
     • $18,888.89 + 5,100 = 23,988.89$ total cash required to close.

Summary of Concepts

• Mortgages involve two components: a promissory note (details amount owed and repayment terms) and a security instrument (collateral for the loan).
• The primary mortgage market involves loan origination, while the secondary market involves the buying and selling of loans.
• Key formulas include multiplication of monthly payments by the number of payments to find total loan cost.
• Points are valued at 1% of the loan amount, impacting interest rates and total costs significantly.