1. Chapter 3: Consumer Math
Section 3.5: Mortgages
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

2. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Amortization
Amortization is a situation in which the borrower agrees to make regular payments on the principal and interest until a loan is paid off. Payments can be calculated using tables of numbers, spreadsheets (formulas), or calculators (physical or online). Be sure to round money to the cent. Amortization tables are usually pretty big – think book-sized. The following table is just a small sample for five different rates and three different terms. To find the amount of the monthly mortgage payment, look up the entry corresponding to the APR and the term, and then multiply by the amount borrowed and divide by 1000.
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

3. Amortization
Example: Use the table provided to find the monthly payment (MP) for a $184,000 loan at 5.5% for 30 years.
MP = × $184,000 ÷ 1000
MP = $  $
Monthly Mortgage Payment per $1000 Borrowed
Rate (%)
15 Years
20 Years
30 Years
4.50
7.6499
6.3265
5.0669
5.00
7.9079
6.5996
5.3682
5.50
8.1708
6.8789
5.6779
6.00
8.4386
7.1643
5.9955
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

4. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Amortization
If you are planning to purchase a home, get an app for your phone or visit a website with an online mortgage (or amortization) calculator. There are thousands to choose from. Most online calculators are very easy to use. Some will even calculate the payment including taxes and insurance. One very simple amortization calculator found at Just remember to click the “Calculate” button after you enter your data. It is important to note that we should NOT change the interest rate to a decimal for use in the online calculator. That is, if the APR is 3.5%, use 3.5 and not
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

5. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Amortization
Example: Use a mortgage calculator to find the monthly payment for $200,000 financed at 3.5% for 30 years. And, assuming that exact amount is paid for every payment, what will be the total amount paid for this mortgage over the 30-year term?
MP = $898.09
30-Year Total = $323,312.18
How much would the monthly payment change if the loan was financed for 20 years?
MP = $ , which is $ more than the 30-yr term.
20-Year Total = $278,380.66, which is $44, LESS than the 30-yr term.
If you can afford an extra $262 per month, you would save almost $45,000 over the life of the loan.
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

6. The Entire Monthly Payment
Unfortunately, a monthly mortgage payment often has more components that just principal and interest. These additional charges may include
Real Estate Taxes: A percentage of the assessed value of the home.
Homeowner’s Insurance
Homeowner’s Association (HOA) Dues
Private Mortgage Insurance (PMI)
Example: If Lisa’s monthly mortgage payment is $1250, her annual real estate taxes are $1600, and her homeowner’s insurance is $900/year, how much is her entire monthly housing payment?
Be sure to divide the taxes and insurance totals into monthly amounts.
Total Monthly Payment = $ $1600/12 + $900/12 = $ …  $
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

7. Affordability Guidelines
When borrowing money to purchase a home, the lender must decide whether or not to lend the buyer the money.
Different institutions can develop their own own guidelines that can be followed when making lending decisions. We will consider three such guidelines.
Guideline #1: The amount of the mortgage loan should not exceed three times the borrower’s annual gross income.
Guideline #2: If a family has other significant monthly debt obligations, such as car payments, credit cards, or student loans, the family’s monthly housing expenses, including mortgage payment, property taxes, and private mortgage insurance, should be limited to no more than 25% of their monthly gross income (income prior to deductions).
Guideline #3: If the family has no other significant monthly debt obligations, the monthly housing costs could reach as high as 38% of their gross monthly income.
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

8. Affordability Guidelines
IMPORTANT CONCEPT
If we are seeking the maximum mortgage amount, use Guideline #1.
IMPORTANT CONCEPT
If we are seeking the maximum monthly amount for housing expenses, see if other monthly debt obligations exist. If so, use Guideline #2. If not, use Guideline #3.
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

9. Affordability Guidelines
Exercise: Susan has a gross annual income of $75,000. What is the maximum amount she can afford to borrow?
Using Guideline #1: 3($75,000) = $225,000
Exercise: If Susan has no extra significant monthly debt obligations, what is the maximum she can devote to housing expenses each month?
Using Guideline #3: Her MONTLY gross income is $6250.
Max Monthly Housing Expenses = 0.38($6250) = $2375
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates