MA.912.FL.3.9

Compare the advantages and disadvantages of different types of mortgage loans by manipulating a variety of variables and calculating fees and total cost using spreadsheets and other technology.

Clarifications

Clarification 1: Instruction includes understanding various considerations that qualify a buyer for a loan, such as Debt-to-Income ratio. 

Clarification 2: Fees include discount prices, origination fee, maximum brokerage fee on a net or gross loan, documentary stamps and prorated expenses. 

Clarification 3: Instruction includes a cost comparison between a higher interest rate and fewer mortgage points versus a lower interest rate and more mortgage points. 

Clarification 4: Instruction includes a cost comparison between the length of the mortgage loan, such as 30-year versus 15-year. Clarification 5: Instruction includes adjustable rate loans, tax implications and equity for mortgages.

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Financial Literacy
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment


Terms from the K-12 Glossary

 

Vertical Alignment

Previous Benchmarks

Next Benchmarks

 

Purpose and Instructional Strategies

In Math for Data and Financial Literacy, students explore multiple factors that relate to mortgages and examine key factors that influence the ability to obtain mortgages in general. 
  • Point out for students that mortgages are typically the largest loans most adults seek to obtain. Given the scale of the loan, banks are careful to research the capacity and trustworthiness of buyers to be able to repay the loan. If buyers default on mortgage payments, the bank could lose large amounts of money. Given this risk, lenders use various considerations that qualify buyers for a loan. 
    • Debt-to-Income Ratio: 
      This ratio examines a buyer’s margin in their monthly budget to be able to pay for a mortgage. Two ratios are commonly used. Front-end ratios examine the total monthly housing costs for a buyer, including the current mortgage/rent payment, mortgage insurance, homeowner’s insurance, and property taxes. 
      (total monthly housing costs)(monthly gross income) = Front-end Ratio
      Lenders typically look for front-end ratios that are less than 28 percent to approve a mortgage application. Back-end ratios explore the other recurring debts a buyer has each month outside of their housing expenses. These include installment loans, car payments and credit card payments. 
      (total monthly recurring debts)(monthly gross income) = Back-end Ratio 
      Lenders typically look for back-end ratios that are less than 36 percent to approve a mortgage application. 
    • Credit Score 
      Lenders lean heavily on credit scores to determine the trustworthiness of buyers to repay the mortgage. Buyers with poor credit history will have higher interest rates for loans due to the greater risk incurred by the lender. 
    • Down Payment 
      A down payment is an initial payment made at the time of purchase for the home before entering into a mortgage. Down payments increase the trustworthiness of the buyer to the lender because buyer has invested their money in the purchase as well as the lender’s money, which makes it more likely for the buyer to repay the loan. Down payments can lower interest rates for the buyer and increase the chance of being approved for a mortgage. Down payments can be any percentage of the purchase price, but down payments of 20% or more allow buyers to avoid mortgage insurance. 
    • Work History 
      Lenders will check buyers work history to ensure a steady track record of income over a sustained period of time. This helps ensure their ability to repay the loan. 
    • Home Quality 
      Lenders will also require a home inspection before providing a mortgage. If a buyer defaults on the loan, the lender will eventually sell the home to regain as much of the loan amount as possible. For that reason, lenders want to make sure homes are in good condition and will achieve high selling prices should the need arise. 
  • When considering purchasing a home, calculating monthly payments based off of the purchase price is not enough. Additional fees can come into play when purchasing a home that need to be considered. These fees are commonly known as closing costs. 
    • Discount Prices 
      Discount prices depend on the use of discount points (also known as mortgage points). Typically, the cost of one mortgage point equals 1% of the loan amount (some lenders allow for fractions of a percent), and this single point lowers the interest rate of the mortgage by about 0.25%. For example, if the mortgage amount is $250,000 at a 3.5% mortgage rate, a buyer might purchase one mortgage point for $2,500 (paid at closing) to get a 3.25% interest rate instead. The $2,500 paid at closing would be considered the “discount price.” 
    • Origination Fee 
      This fee is paid to the lender to cover the administrative costs for processing the mortgage application. These fees are typically 0.5% to 1% of the loan amount. 
    • Maximum Brokerage Fee 
      Mortgage brokers can be used to help home buyers find and secure a mortgage loan. They explore multiple lenders and loan options in pursuit of the best deal for the buyer. Their service typically comes at a cost of 1% to 2% of the loan amount. Depending on the quality of the loan they generate, this might be a worthwhile investment. 
    • Documentary Stamps 
      Homes come with a title, which identifies the owner or the home and property. When purchasing a home, the home title will be transferred to a new owner. This documentation requires the payment of a transfer fee. In Florida, this fee is called the “Florida documentary stamp tax.” This fee is calculated at $0.35 for every $100 of the purchase price. 
    • Prorated Expenses 
      At closing, there are several expenses that the seller of the home has been paying that need to be transferred to the buyer. Proration is the process of dividing various property expenses between the buyer and seller in a way that allows each party to only pay for the time they own the property. These expenses include property taxes, homeowner’s insurance, home owner’s association dues and mortgage interest. As an example, sellers who have paid for a full year’s worth of property tax but are selling their home before the end of the year will have the “unused” amount added to closing costs so they get it refunded to them. The buyer pays this amount at closing and, in essence, pays the property tax for the remainder for the year. 
  • After introducing the idea of mortgage points to students, have them perform a cost comparison between a higher interest rate and fewer mortgage points versus a lower interest rate and more mortgage points. Highlight the idea that the use of mortgage points, especially on longer term loans, can generate significant savings in interest payments. 
    • For example, Tonya takes out a $260,000 30-year fixed-rate mortgage at 4.2%. Her lender offers an interest rate of 3.7% if she purchases 2 mortgage points. On a $260,000 loan, two points would cost an additional $5,200 at closing. Is this a good deal? 
    • If Tonya chooses not to buy mortgage points, her interest rate will remain at 4.2%. Over 30 years, without paying down the loan early, the cost of the loan, with interest, is $455,739.98. However, if she purchases two mortgage points, she would pay $429,333.18 over the life of the loan. This means that buying mortgage points saved Tonya $26,406.80 over the course of her mortgage. 
  • Instruction includes a cost comparison between lengths of mortgage loans, such as 30year, 20-year and 15-year. Students should discover that shorter term loans will have higher monthly payments but smaller total interest charges. Have students discuss (MTR.5) the advantages and disadvantages of each. Consider guiding students to examine following comparison: 
    • Compare the monthly payment and total interest payment for a $320,000 mortgage at 3.41% for 15-, 20-and 30-year terms. 

  • Instruction addresses adjustable rate loans, tax implications and equity for mortgages. 
    • Adjustable Rate Loans 
      Adjustable rate mortgages (ARMs) carry interest rates that shift (adjust) at a prearranged frequency over time. They typically have terms of 30 years. These mortgages can start with lower interest rates than fixed rate mortgages, but over time will adjust to have higher interest rates than fixed rate mortgages. 
    • ARMs have additional variables that require the introduction of some new terminology: 
      • Adjustment Frequency 
        The time between interest rate adjustments. Typically, this will start with a long introductory interval such as 5 or 10 years and then shift to shorter intervals such as 6 months. For this reason, frequencies are communicated with two numbers such as 7y/6m, which represents a 7-year introductory interval followed by 6-month adjustment intervals. 
      • Adjustment Index 
        This is a benchmark used to set the interest rates. Many lending institutions use the Secured Overnight Financing Rate (SOFR) as their index. 
      • Margin 
        Buyers who use an ARM agree to pay an interest rate that is a constant percentage above the Adjustment Index. This amount is called the margin. 
      • Caps 
        The limit an interest rate can increase each adjustment period. Some loans feature a higher initial adjustment cap followed by a smaller cap for the shorter adjustment intervals. Other loans may show an overall cap for the life of the loan. Add this to the introductory interest rate to find the ceiling. 
      • Ceiling 
        The highest an interest rate allowed for the life of the loan. 
    • Adjustable Rate Mortgages are rarely a good idea for long-term home buyers since the interest rates will eventually rise above fixed rates. ARMs are typically purchased by home buyers who plan to sell their home before the end of the introductory interval. 
    • Tax Implications 
      Buying and owning a home does bring some tax benefits for the buyer/owner. Mortgage point costs, mortgage interest payments, and property taxes are tax deductible and can reduce the total amount of income you pay taxes on each year. 
    • Equity 
      Equity refers to the difference in what a buyer owes for their home and the home’s present value. For a buyer who pays a 20% down payment for a home worth $200,000, they would have $40,000 in equity in the home at the time of purchase. Their equity in the home increases as mortgage payments reduce the principal of the mortgage. Equity can also increase as the value of the home increases. If home values fall, equity in the home decreases as a result. 
  • Instructions includes other mortgages such as Federal Housing Administration (FHA) and U.S. Department of Agriculture (USDA) and situations when one may need to have one of these loans.
 

Common Misconceptions or Errors

  • Students may not consider homeowner’s insurance, property taxes or Private Mortgage Insurance (if making a down payment less that 20%) when considering how much of a mortgage they can afford for a given budget. 
  • Students may not consider that both front-end and back-end ratios are considered by lenders. Budgets that have too large of a back-end ratio will not be eligible for many loans even if the front-end ratio is under 28%. 
  • If considering an ARM, student may assume the adjustment index rate will remain constant over time. Heavy research should be done on the historical fluctuation of adjustment index rates before assuming the risk of an ARM.
 

Instructional Tasks

Instructional Task 1 (MTR.4.1, MTR.6.1
  • You’re planning to buy your first home. The house you want is listed at $240,000. You’ve saved enough to make a 10% down payment. Closing costs will total 4% of the purchase price and PMI will cost you $117 each month. Assuming your budget will allow for up to $1,500 a month in mortgage expenses after paying property taxes and homeowner’s insurance, analyze the following purchase options and list the advantages and disadvantages of each. 
    • A 30-year fixed rate mortgage at 2.75%. 
    • A 30-year fixed rate mortgage at 2.25% after using 2 mortgage points. 
    • A 20-year fixed rate mortgage at 2.625%. 
    • A 7y/6m ARM (30-year term) with a 2.125% introductory rate, a margin of 2.75% over SOFR (currently at 0.05%), 5% first adjustment cap, 1% subsequent adjustment cap and a lifetime cap of 5%.
 

Instructional Items

Instructional Item 1
  • You and your spouse are applying for a mortgage with a local bank, who will check your front-end and back-end ratio before approving the loan. Your combined take home income is $98,756. The monthly mortgage for the house you want is $1,496 each month. The annual property taxes would be $1,825 and your homeowner’s insurance premium would cost $1,114 each year. You have two car payments, one $578 per month and the other $456 per month, and one student loan payment of $272 each month. Based on these expenses, would the bank approve your loan? Why or why not?

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

Related Courses

This benchmark is part of these courses.
1200388: Mathematics for Data and Financial Literacy Honors (Specifically in versions: 2022 and beyond (current))
1200384: Mathematics for Data and Financial Literacy (Specifically in versions: 2022 and beyond (current))
7912120: Access Mathematics for Data and Financial Literacy (Specifically in versions: 2022 - 2023, 2023 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.912.FL.3.AP.9: Given two different mortgage loans, one 15-year and one 30-year, compare the advantages and disadvantages of each loan’s interest rate, monthly payment and total cost.

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