CHAPTER 8 Personal Finance

The Cost of Home Ownership 8.7 The Cost of Home Ownership

Objectives Compute the monthly payment and interest costs for a mortgage. Prepare a partial loan amortization schedule. 3. Solve problems involving what you can afford to spend for a mortgage. 4. Understand the pros and cons of renting versus buying.

Mortgages A mortgage is a long-term loan for the purpose of buying a home. The down payment is the portion of the sale price of the home that the buyer initially pays to the seller. The amount of the mortgage is the difference between the sale price and the down payment. Some companies, called mortgage brokers, offer to find you a mortgage lender willing to make you a loan. Fixed-rate mortgages have the same monthly payment during the entire time of the loan. Variable-rate mortgages known as adjustable-rate mortgages (ARMs), have payment amounts that change from time to time depending on changes in the interest rate.

Computations Involved with Buying a Home Most lending institutions require the buyer to pay one or more points at the time of closing—that is, the time at which the mortgage begins. A point is a one-time charge that equals 1% of the loan amount. For example, two points means that the buyer must pay 2% of the loan amount at closing. A document, called the Truth-in-Lending Disclosure Statement, shows the buyer the APR for the mortgage. In addition, lending institutions can require that part of the monthly payment be deposited into an escrow account, an account used by the lender to pay real estate taxes and insurance.

Computation Involved with Buying a Home Loan Payment Formula for Fixed Installment Loans The regular payment amount, PMT, required to repay a loan of P dollars paid n times per year over t years at an annual rate r is given by

Example: Computing the Monthly Payment and Interest Costs for a Mortgage The price of a home is $195,000. The bank requires a 10% down payment and two points at the time of closing. The cost of the home is financed with a 30-year fixed rate mortgage at 7.5%. Find the required down payment. Find the amount of the mortgage. How much must be paid for the two points at closing? Find the monthly payment (excluding escrowed taxes and insurance). Find the total interest paid over 30 years.

Example: Computing the Monthly Payment and Interest Costs for a Mortgage Solution: The required down payment is 10% of $195,000 or 0.10  $195,000 = $19,500. The amount of the mortgage is the difference between the price of the home and the down payment.

Example: Computing the Monthly Payment and Interest Costs for a Mortgage To find the cost of two points on a mortgage of $175,500, find 2% of $175,500. 0.02  $175,500 = $3510 The down payment ($19,500) is paid to the seller and the cost of two points ($3510) is paid to the lending institution.

Example: Computing the Monthly Payment and Interest Costs for a Mortgage We need to find the monthly mortgage payment for $175,500 at 7.5% for 30 years. We use the loan payment formula for installment loans. The monthly mortgage payment for principal and interest is approximately $1227.00.

Example: Computing the Monthly Payment and Interest Costs for a Mortgage e. The total cost of interest over 30 years is equal to the difference between the total of all monthly payments and the amount of the mortgage. The total of all monthly payments is equal to the amount of the monthly payment multiplied by the number of payments. We found the amount of each monthly payment in (d): $1227. The number of payments is equal to the number of months in a year, 12, multiplied by the number of years in the mortgage, 30: 12  30 = 360. Thus, the total of all monthly payments = $1227  360.

Example: Computing the Monthly Payment and Interest Costs for a Mortgage Now we calculate the interest over 30 years. The total interest paid over 30 years is approximately $266,220.

Loan Amortization Schedules When a loan is paid off through a series of regular payments, it is said to be amortized, which literally means “killed off.” Although each payment is the same, with each successive payment the interest portion decreases and the principal portion increases. A document showing important information about the status of the mortgage is called a loan amortization schedule.

Example: Preparing a Loan Amortization Schedule Prepare a loan amortization schedule for the first two months of the mortgage loan shown in the following table:

Example: Preparing a Loan Amortization Schedule Solution: We begin with payment number 1. Interest for the month = Prt = $130,000  0.095  1/12 ≈ $1029.17 Principal payment = Monthly payment  Interest payment = $1357.50  $1029.17 = $328.33 Balance of loan = Principal balance  Principal payment = $130,000  $328.33 = $129,671.67

Example: Preparing a Loan Amortization Schedule Now, starting with a loan balance of $129,671.67, we repeat these computations for the second month. Interest for the month = Prt = $129,671.67  0.095  1/12 = $1026.57 Principal payment = Monthly payment – Interest payment = $1357.50 – $1026.57 = $330.93 Balance of loan = Principal balance – Principal payment = $129,671.67 – $330.93 = $129,340.74

Example: Preparing a Loan Amortization Schedule

What Can You Afford Here’s the bottom line from most financial advisers: • Spend no more than 28% of your gross monthly income for your mortgage payment. • Spend no more than 36% of your gross monthly income for your total monthly debt, including mortgage payments, car payments, credit card bills, student loans, and medical debt.

Maximum Amount You Can Afford

Example: What Can You Afford? Suppose that your gross annual income is $25,000. a. What is the maximum amount you should spend each month on a mortgage payment? b. What is the maximum amount you should spend each month for total credit obligations? c. If your monthly mortgage payment is 80% of the maximum amount you can afford, what is the maximum amount you should spend each month for all other debt? Round all computations to the nearest dollar.

Example: (cont) Suppose that your gross annual income is $25,000. a. What is the maximum amount you should spend each month on a mortgage payment? With a gross annual income of $25,000, your gross monthly income is $25,000/12 = $2083. You should spend no more than 28% of your gross monthly income, $2083, on a mortgage payment. 28% of $2083 = 0.28($2083) ≈ $583.

Example: (cont) Suppose that your gross annual income is $25,000. b. What is the maximum amount you should spend each month for total credit obligations? With a gross annual income of $25,000, your gross monthly income is $25,000/12 = $2083. You should spend no more than 36% of your gross monthly income, $2083, for total monthly debt. 36% of $2083 = 0.36($2083) ≈ $750.

Example: (cont) c. If your monthly mortgage payment is 80% of the maximum amount you can afford, what is the maximum amount you should spend each month for all other debt? This means that your monthly mortgage payment is 80% of $583. 80% of $583 = 0.8($583) = $466. In part (b), we saw that your total monthly debt should not exceed $750. Because you are paying $466 for your mortgage payment, this leaves $750 − $466, or $284, for all other debt. Your monthly credit obligations, excluding mortgage payments, should not exceed $284.

Renting versus Buying Benefits of Renting No down payment or points are required. You generally have a security deposit that is returned at the end of your lease. Very mobile: You can easily relocate, moving as often as you like and as your lease permits. Does not tie up hundreds of thousands of dollars that might be invested more safely and lucratively elsewhere. Most financial advisers agree that you should buy a home because you want to live in it, not because you want to fund your retirement. Does not clutter what you can afford for your total monthly debt with mortgage payments.

Renting versus Buying Benefits of Renting May involve lower monthly expenses. You pay rent, whereas a homeowner pays the mortgage, taxes, insurance, and upkeep. Can provide amenities like swimming pools, tennis courts, and health clubs. Avoids the risk of falling housing prices. Does not require home repair, maintenance, and groundskeeping. There are no property taxes. Generally less costly than buying a home when staying in it for fewer than three years.

Renting versus Buying Benefits of Home Ownership Peace of mind and stability. Provides significant tax advantages, including deduction of mortgage interest and property taxes. There is no chance of rent increasing over time. Allows for freedom to remodel, landscape, and redecorate. You can build up equity, the difference between the home’s value and what you owe on the mortgage, as the mortgage is paid off. The possibility of home appreciation is a potential source of cash in the form of home equity loans.

Renting versus Buying Benefits of Home Ownership When looking at seven-year time frames, the total cost of renting (monthly rent, renter’s insurance, loss of potential interest on a security deposit) is more than twice the total cost of buying for home owners who itemize their tax deductions.