632 CHAPTER 10 Consumer Mathematics Lenders typically use a formula to determine the maximum monthly payment that they believe the buyer can reasonably pay based on the buyer’s monthly income and the buyer’s other monthly debt payments. Other monthly debt payments considered are usually car payments, student loan payments, other fixed installment loan payments, and credit card payments. The buyer’s monthly income before any deductions is called the gross monthly income . From the gross monthly income subtract any monthly debt payments with more than 10 monthly payments remaining to obtain the buyer’s adjusted monthly income . Generally, a mortgage loan officer will multiply the adjusted monthly income by 28% In general, this product is the maximum monthly house payment the lending institution believes that the purchaser can afford to pay. This payment must cover principal, interest, property taxes, and insurance. Taxes and insurance are not necessarily paid to the bank; they may be paid directly to the tax collector and the insurance company, respectively. Example 2 shows how a bank uses the formula to determine whether a prospective buyer qualifies for a mortgage. Example 2 Qualifying for a Mortgage Suppose the Martins’ (see Example 1) gross monthly income is $7250 and they have 23 remaining monthly payments of $225 on their car loan, 17 remaining monthly payments of $175 on their daughter’s orthodontic braces, and 11 remaining monthly payments of $45 on a loan used to purchase new furniture. The property taxes and homeowners’ insurance on the house they wish to buy are $165 and $115 per month, respectively. Their bank will approve a loan that has a total monthly mortgage payment of principal, interest, property taxes, and homeowners’ insurance that is less than or equal to 28% of their adjusted monthly income. a) Determine 28% of the Martins’ adjusted monthly income. b) The Martins want a 30-year, $211,650 mortgage. If the interest rate is 4.0% determine the total monthly house payment (including principal, interest, property taxes, and homeowners’ insurance) for this mortgage. c) Determine whether the Martins qualify for this mortgage. Solution a) To determine the Martins’ adjusted monthly income, subtract the sum of their monthly payments, $225 $175 $45 $445, + + = from their gross monthly income, $7250. $7250 445 $6805 − Gross monthly income Monthly payments Adjusted monthly income Next, take 28% of the adjusted monthly income. 0.28 $6805 $1905.40 × = Thus, 28% of the Martins’ adjusted monthly income is $1905.40. b) To determine the total monthly house payment, we first need to determine the monthly principal and interest payments. Then we add the monthly property taxes and homeowners’ insurance. We will use a table to calculate the monthly principal and interest payments the Martins will need to pay. Table 10.4 gives monthly principal and interest payments per $1000 of mortgage. With an interest rate of 4.0% and a 30-year mortgage, the Martins would have a monthly principal and interest payment of $4.77415 (circled in blue) per thousand dollars of mortgage. To determine the Martins’ monthly principal and interest payment on their mortgage, first divide the mortgage amount by $1000, which will give the number of thousands of dollars of the mortgage. $211,650 $1000 211.65 = MATHEMATICS TODAY Credit Scores When consumers borrow money by obtaining car loans, home mortgages, or other loans or through the use of credit cards, the lender takes a risk by giving money to the borrower in exchange for the borrower’s promise to repay the loan plus interest. To minimize their risk, lenders do research on borrowers to determine the likelihood the borrowers will default, or fail to repay the loans. Lenders often obtain this research from a consumer credit bureau. Credit bureaus assign a credit score to an individual after researching the individual’s credit history, income, age, and other factors. A high credit score suggests that the individual is more likely to repay a loan and often enables the borrower to get lower interest rates on loans. The three largest credit bureaus are Equifax, Experian, and TransUnion. All three bureaus use a credit score called a FICO score. Score Credit Outlook 800 –850 Excellent rating; low interest rates 740 –799 Very good rating, but short of excellent 670 –739 Good rating; moderate risk 580 – 669 Fair rating; higher risk and high interest rates 300 –579 Poor rating; highest risk; may not qualify for loans Source: Equifax.com Why This Is Important Preserving a good credit rating is essential for consumers who wish to obtain a mortgage, a credit card, or other borrowing opportunities.
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