Contemporary Mathematics

# 6.12Renting and Homeownership

Contemporary Mathematics6.12 Renting and Homeownership

Figure 6.26 Purchasing a home is a big investment, while renting is a lower cost alternative. (credit: "New construction, new development house for sale" by jongorey/houseandhammer.com, CC BY 2.0)

## Learning Objectives

After completing this section, you should be able to:

3. Calculate the monthly payment for a mortgage and related interest cost.
4. Read and interpret an amortization schedule.
5. Solve application problems involving affordability of a mortgage.

After renting an apartment for 10 years, you realize that it may be time to purchase a home. Your job is stable, and you could use more space. It is time to investigate becoming a homeowner. What are the things that you must consider, and what is the financial benefit of owning as opposed to renting? This section is about the advantages, disadvantages, and costs of homeownership as opposed to renting.

When renting, you will likely sign a lease, which is a contract between a renter and a landlord. A landlord is the person or company that owns property that is rented. The lease will detail your responsibilities, restrictions on activities, deposits, fees, maintenance, repairs, and rent during the term of the lease. It also defines what your landlord can, and cannot, do with the property while you occupy the property.

• Lower cost.
• Short-term commitment.
• Little to no maintenance cost. The landlord pays for or performs most maintenance.
• You need not stay at end of lease. Once the lease term is over (the lease is up), you are not obligated to stay.
• If renting in an apartment complex, there may be a pool, gym, or community room for renters to use.

Of course, there are disadvantage too:

• No tax incentives.
• Housing cost is not fixed. When the lease is up, the rent can change.
• No equity. When you are done living in a rental, you have built no value.
• Restrictions on occupants. There may be a limit on how many can live in the apartment.
• Restrictions on decorating. The property is not yours, so any decorating or improvements need landlord permission.
• Limits on pets. Permission for pets, and their number and type, will be set forth in the lease.
• May not be able to remain when lease term is over. The landlord can, at the end of your lease, invite you to leave.
• The building may be sold, and the new landlord may institute changes to the lease when the previous lease expires.

Renting has fees to be paid at the start of the lease. Typically, when you rent, you will pay first and last months’ rent and a security deposit. A security deposit is a sum of money that the landlord holds until the renter leaves the rental property. The deposit will cover repairs for damage to the apartment during the renter’s stay but may be returned if the apartment is in good condition. If your landlord runs a credit check on you, the landlord may charge you for that.

• There are tax incentives. The interest you pay for your mortgage (more on that later) is deductible on your federal income tax.
• There are no restrictions on pets or occupants, unless laws in your area specify limits for homes.
• You can redecorate any way you wish, limited only by the laws in your area.
• Once your mortgage is set with a fixed-interest rate, your housing cost is fixed.
• Your home grows equity, that is, the difference between what you owe and what the house is worth grows. You can use the equity to secure loans, and you recover the equity (and more if you’re fortunate) when you sell the house.
• As long as you pay your mortgage and maintain the home to the standards of your community, you can stay as long as you wish.

Some disadvantages to home ownership are:

• The cost is higher than renting. Mortgages and associated costs are typically higher than rent for a similar living space.
• The owner is responsible for upkeep, maintenance, and repairs. These can be extremely costly.
• The owner cannot walk away from the property. It can be sold, but simply leaving the property, especially if not paid off yet, has serious consequences.

The big question of affordability looms large over the decision to rent or buy. Renting, strictly from an affordability viewpoint, comes with much less initial outlay and smaller commitment. If you do not have sufficient income to regularly save for possibly expensive repairs, or your credit isn’t quite as good as it needs to be, then renting may be the best choice. Of course, even if you can afford to buy a home, you may choose to rent based on the comparative advantages.

## Video

Buying a home really involves two buyers. You and the mortgage company. The mortgage company has interest in the home, as they are providing the funds for the home. They want to protect their investment, and many fees are about the bank as much as the buyer. They fund a mortgage based on the value they assign the property. Not you. This means they will want some certainty that the home is sound, and you are a good investment.

## Who Knew?

### Closing Costs

When a home is bought, there are many costs that need to be paid at the time of purchase, which are lumped under the term closing costs. At the start of 2022, the average closing costs for a single-family home exceeded $6,800. These costs include: • The appraisal fee, which is what is paid to someone to establish the home’s worth. The value of the home to the bank may differ from what the home is listed for, or what an app tells you the home is worth. It may run approximately$350.
• The home inspection fee. The inspection should reveal any problems with the house that will need to be fixed either before or after you obtain the home.
• The title search. The is a records search to insure there are no issues with who actually owns the property. It can cost about 0.5% to 1% of the amount you are financing.
• Prepaid taxes. You will need to pay about 6 months of taxes at the time of purchase.

1.

1.

1.

Figure 6.27 shows a portion of an amortization table for a 30-year, $165,900 mortgage. Use that table to answer the following questions. 1. What is the interest rate? 2. How much are the payments? 3. How much of payment 175 goes to principal? 4. How much of payment 180 goes to interest? 5. What’s the remaining balance on the mortgage after payment 170? Figure 6.27 Amortization table ## Your Turn 6.113 Below is a portion of an amortization table for a 30-year,$228,320 mortgage. Use that table to answer the following questions.
Amortization table
1.
What is the interest rate?
2.
How much are the payments?
3.
How much of payment 235 goes to principal?
4.
How much of payment 215 goes to interest?
5.
What’s the remaining balance on the mortgage after payment 227?
6.
At what payment does the amount that is applied to mortgage finally exceed the amount applied to interest?

## Escrow Payments

The last few examples have looked at mortgage payments, which cover the principal and interest. However, when you take out a mortgage, the payment is sometimes much higher than that. This is because your mortgage company also has you pay into an escrow account, which is a savings account maintained by the mortgage company.

Your insurance payments will be set by your insurer and the mortgage company will pay them on time for you from your escrow account. Your property taxes are set by where you live and are typically a percentage of your property’s assessed value. The assessed value is the estimation of the value of your home and does not necessary reflect the purchase or resale value of the home. Your property taxes will also be paid on time by the mortgage company from your escrow account.

For example, in Kalamazoo, Michigan, the effective tax rate for property is 1.69% of the assessed value of the home. These escrow payments, which cover bills for the home, can increase the monthly payments for your home well beyond the basic principal and interest payment.

Jenna decides to purchase a home, with mortgage of $108,450 at 6% interest for 30 years. The assessed value of her home is$75,600. Her property taxes come to 5.7% of her assessed value. Jenna also has to pay her home insurance every 6 months, which is $744 per six months. How much, including escrow, will Jenna pay per month? ## Your Turn 6.114 1. Destiny decides to purchase a home, with mortgage of$159,195.50 at 5.75% interest for 30 years. The assessed value of her home is $100,000. Her property taxes come to 5.42% of her assessed value. Destiny also has to pay her home insurance every 6 months, and that comes to$843 per 6 months. How much, including escrow, will Destiny pay per month?

78.
79.
Which has more restrictions, renting or buying?
80.
Which has housing cost that does not change?
81.
What is the name given to a loan for a home?
82.
What are the monthly payments for a 30-year mortgage of $108,993 with 6.14% interest. 83. What is the cost of financing for a 30-year mortgage of$108,993 with 6.14% interest if the mortgage is paid off?
84.
Consider the following amortization table. What is the amount of payment 141 that goes to principal?
85.
What is the name of the account that the mortgage company holds your taxes and insurance in?

## Section 6.12 Exercises

In the following exercises, indicate if the advantage listed is for renting or buying a home.
1 .
Short-term commitment.
2 .
3 .
Freedom to remodel.
4 .
Builds equity.
5 .
Cost is lower.
6 .
You do not pay for repairs.
7 .
No pet restrictions
8 .
More flexibility to move.
9 .
Housing cost is fixed.
10 .
May have other amenities.
In the following exercises, find the mortgage payment for the given loan amount, interest rate, and term.
11 .
Loan amount is $78,560, interest rate is 5.87%, 30-year mortgage. 12 . Loan amount is$125,800, interest rate is 6.5%, 30-year mortgage.
13 .
Loan amount is $96,400, interest rate is 4.9%, 15-year mortgage. 14 . Loan amount is$267,450, interest rate is 5.25%, 20-year mortgage.
In the following exercises, find the total paid on the mortgage if it is fully paid through the term.
15 .
Loan amount is $78,560, interest rate is 5.87%, 30-year mortgage. 16 . Loan amount is$125,800, interest rate is 6.5%, 30-year mortgage.
17 .
Loan amount is $96,400, interest rate is 4.9%, 15-year mortgage. 18 . Loan amount is$267,450, interest rate is 5.25%, 20-year mortgage.
In the following exercises, find the cost of financing for the mortgages if they are fully paid.
19 .
Loan amount is $78,560, interest rate is 5.87%, 30-year mortgage. 20 . Loan amount is$125,800, interest rate is 6.5%, 30-year mortgage.
21 .
Loan amount is $96,400, interest rate is 4.9%, 15-year mortgage. 22 . Loan amount is$267,450, interest rate is 5.25%, 20-year mortgage.
In the following exercises, use the amortization table to answer the question.
23 .
What is the term of the mortgage?
24 .
How much of payment 165 applies to interest?
25 .
What is the remaining balance after payment 155?
26 .
How much total interest was paid after payment 149?
In the following exercises, use the amortization schedule to answer the question.
27 .
What is the interest rate for the mortgage?
28 .
How much of payment 110 applies to principal?
29 .
What is the remaining balance after payment 94?
30 .
How much total interest was paid after payment 111?
In the following exercises, find the total monthly payment including both the mortgage payment and the escrow payment.
31 .
Mortgage of $87,690 at 6.2% interest for 30 years. Assessed value of the home is$75,600. Property taxes come to 5.65% of assessed value. Home insurance of $815 paid every 6 months. 32 . Mortgage of$143,900 at 5.05% interest for 30 years. Assessed value of the home is $90,150. Property taxes come to 5.88% of assessed value. Home insurance of$924 paid every 6 months.
33 .
Mortgage of $65,175 at 6.48% interest for 30 years. Assessed value of the home is$62,800. Property taxes come to 6.75% of assessed value. Home insurance of $558 paid every 6 months. 34 . Mortgage of$245,950 at 5.35% interest for 30 years. Assessed value of the home is $156,500. Property taxes come to 6.41% of assessed value. Home insurance of$972 paid every 6 months.
For the following exercises, read the following: Fifteen-year mortgage compared to 30-year mortgage. Mortgage interest rates are often higher for 30-year mortgages than 15-year mortgages. However, the payments for 15-year mortgages are considerably higher. The following exercises explore the difference between a 15- and 30-year mortgage for a mortgage of $100,000. 35 . The 15-year mortgage interest rate is 5.65%. 1. Find the payment. 2. Determine the total that would be paid if the mortgage was completed. 3. Find the cost of financing for this mortgage. 36 . The 30-year mortgage rate is 6.4%. 1. Find the payment. 2. Determine the total that would be paid if the mortgage was completed. 3. Find the cost of financing for this mortgage. 37 . How different are the payments, the total paid, and the cost to finance? 38 . Summarize the answer in the previous question. For the following exercises, read the following: Fifteen-year mortgage compared to 30-year mortgage. A 15-year mortgage comes with advantages, the biggest being the home is paid off much sooner, and equity is built much more quickly. Mortgage interest rates are often higher for 30-year mortgages than 15-year mortgages. However, the payments for 15-year mortgages are considerably higher. The following exercises explore the difference between a 15- and 30-year mortgage for a mortgage of$200,000.
39 .
The 15-year mortgage interest rate is 5.6%.
1. Find the payment.
2. Determine the total that would be paid if the mortgage was completed.
3. Find the cost of financing for this mortgage.
40 .
The 30-year mortgage rate is 6.25%.
1. Find the payment.
2. Determine the total that would be paid if the mortgage was completed.
3. Find the cost of financing for this mortgage.
41 .
How different are the payments, the total paid, and the cost to finance?
42 .
Summarize the answer in the previous question.
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