15.8: Home Ownership
- Page ID
- 185431
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- Evaluate the advantages and disadvantages of homeownership.
- Calculate the monthly mortgage payment and the associated interest cost.
- Determine the outstanding balance, partway through the mortgage term, of the remaining future payments.
- Solve application problems related to mortgage affordability.
After renting an apartment for 10 years, you realize it may be time to purchase a home. Your job is stable, and you could use more space. Now is the time to explore the possibility of becoming a homeowner. What factors should you consider, and what are the financial benefits of owning versus renting? We will examine the advantages, disadvantages, and costs of homeownership compared to renting.
Advantages and Disadvantages of 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 the property being rented. The lease outlines 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 it.
Like leasing a car, there are advantages to renting - but also some disadvantages.
Some advantages of renting include:
- Lower cost.
- Short-term commitment.
- Little to no maintenance costs - landlords typically pay for or perform most maintenance.
- No obligation to stay after the lease ends. Once the lease term is over, you are free to move out.
- Access to amenities. Apartment complexes may offer a pool, gym, or community room for residents.
Of course, there are disadvantages as well:
- No tax incentives.
- Housing costs may increase. When the lease is up, the rent can go up.
- No equity. Rent payments do not build ownership or value.
- Restrictions on occupants. There may be limits on how many people can live in the apartment.
- Restrictions on decorating. Because the property isn’t yours, any decorating or improvements typically require landlord approval.
- Limits on pets. Pet policies - including type, number, and permissions - are usually specified in the lease.
- Uncertain long-term availability. At the end of the lease, the landlord may choose not to renew it.
- Property sale risk. If the building is sold, the new landlord may implement changes once the current lease expires.
Renting also includes upfront fees. Typically, you’ll pay the first and last months’ rent plus a security deposit at the start of the lease. The security deposit is held by the landlord to cover any damage to the apartment during your stay and may be refunded if the apartment is left in good condition. If the landlord runs a credit check, you may also be charged a fee for that.
Advantages and Disadvantages of Buying a Home
The advantages of buying a home often mirror the disadvantages of renting, and the disadvantages of homeownership often mirror the advantages of renting.
Some advantages of buying a home include:
- Tax incentives. The interest you pay on your mortgage (more on that later) is deductible on your federal income tax.
- Fewer restrictions. There are generally no limits on pets or occupants unless local laws specify otherwise.
- Freedom to redecorate. You can renovate or decorate however you like, subject only to local regulations.
- Fixed housing costs. Once your mortgage is set with a fixed interest rate, your monthly payments remain stable.
- Equity growth. Your home builds equity - the difference between what you owe and what the house is worth. You can borrow against this equity or recover it (and possibly more) when you sell the home.
- Long-term stability. As long as you pay your mortgage and maintain the home to community standards, you can stay as long as you wish.
Some disadvantages of homeownership include:
- Higher costs. Mortgages and related expenses are often higher than rent for a comparable space.
- Responsibility for maintenance. The homeowner is responsible for upkeep, repairs, and maintenance - some of which can be very costly.
- Lack of mobility. You can’t simply leave the property without serious consequences, especially if the mortgage isn't fully paid off. Selling takes time and comes with its own costs.
The question of affordability looms large in the decision to rent or buy. From a purely financial standpoint, renting generally requires a lower initial outlay and a smaller commitment. If you don't have enough income to regularly save for potential repairs, or if your credit isn't strong enough to qualify for favorable mortgage terms, renting may be the better choice. That said, even if you can afford to buy a home, you may still choose to rent depending on your lifestyle and preferences. Ultimately, you must weigh your options and carefully consider your priorities when deciding whether to rent or buy a home.
Buying a home really involves two buyers: you and the mortgage company. The mortgage company has an interest in the home because they are providing the funds for the purchase. They want to protect their investment, and many of the associated fees are as much about the bank as they are about the buyer. The lender funds a mortgage based on the value they assign to the property, not the value you assign. This means they will want assurance that the home is structurally sound and that you are a reliable investment.
Initial Expenses - Closing Costs
When a home is purchased, there are many costs that must be paid at the time of closing. These are commonly referred to as closing costs. At the start of 2022, the average closing costs for a single-family home exceeded $6,800. These costs may include:
- Appraisal fee: This is paid to a professional who establishes the home’s market value. The value determined by the lender may differ from the listing price or estimates from real estate apps.
- Home inspection fee: This pays for an inspection to uncover any issues with the property that may need to be addressed before or after the purchase.
- Title search: This is a records search to ensure there are no ownership disputes or claims on the property. It typically costs about 0.5% to 1% of the amount being financed.
- Prepaid property taxes: Buyers are often required to prepay about six months of property taxes at the time of purchase.
- Credit report fee: This covers the cost of pulling your credit report.
- Origination fee: Charged by the mortgage company to cover the cost of processing the loan. This fee could range from 0.5% to 1% (or more) of the loan amount.
- Application fee: A processing fee that may amount to several hundred dollars.
- Underwriting fee: This covers the cost of verifying your financial qualifications. It may be a flat fee or a percentage of the loan, such as 0.5% to 1%.
- Attorney fees: If you hire an attorney to assist with the closing, their services will come at an additional cost.
- State or local fees: These may include filing or recording fees charged by your county or municipality.
That’s a long list - and it’s not even complete. When buying a home, be prepared for these costs, as they can come as a surprise. However, in the end, you'll gain equity in the property, meaning when you sell your home, you’ll likely recover some of that investment.
When you purchase a home, you will be required to make a down payment. This means you have money invested in the property, which lenders believe makes you less likely to walk away from it. The amount of the down payment is determined between you and the mortgage company. However, if your down payment is less than 20% of the property’s value, you will be required to pay private mortgage insurance (PMI). This is insurance you pay to protect the mortgage lender in case you default on the loan. PMI typically costs between 0.5% and 2.25% of the original loan amount and increases your monthly mortgage payment. Once you reach 20% equity in the home, you can request that the PMI be removed. Even if you do not make a request, the PMI will eventually be canceled automatically.
Points, also known as discount points, are a financial tool borrowers can use to lower their mortgage interest rate. Each point generally costs 1% of the loan amount and reduces the interest rate by approximately 0.25%, though this can vary by lender and market conditions. Unlike origination fees, points act as a prepayment of interest, allowing borrowers to “buy down” their rate. This strategy can be advantageous for those planning to keep their mortgage long-term, as the upfront cost may be offset by interest savings over time.
Deciding to purchase points requires analyzing the break-even period—the time it takes for interest savings to equal the cost of the points. For instance, if a borrower spends $3,000 on points and saves $50 per month, it would take five years to break even. Borrowers should consider factors like refinancing or selling the property when weighing the benefits of purchasing points.
Mortgages
Some people purchase a home or condo with cash, but the majority apply for a mortgage. A mortgage is a long-term loan in which the property itself serves as collateral. The bank determines the minimum down payment (with your input), the payment schedule, the loan duration, whether the loan can be assumed by another party, and any penalties for late payments. Until the loan is fully repaid, the title of the home belongs to the bank.
Since a mortgage is an installment loan, all the principles from Installment Loans apply, including the formula for calculating payments.
Monthly Mortgage Payments
The PMT formula can be used to calculate the monthly payment of a mortgage loan.
The monthly payment to pay down a mortgage with beginning principal \(P\) is given by the PMT formula with \(n=12\):
\[PMT =\frac{P\left(\frac{r}{12}\right)}{\left[1-\left(1+\frac{r}{12}\right)^{(-12t)}\right]} \nonumber\]
where \(r\) is the annual interest rate (APR) in decimal form and \(t\) is the number of years of the mortgage.
Note: Payments to lenders are always rounded up to the next penny. Do not round numbers during the computation, as rounding introduces errors. You may round only once at the end to report the final answer.
Evan has a 30-year mortgage of $132,650 with an interest rate of 4.8%. Find Evan’s monthly payment.
- Solution
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\(P= \$132,650,~ r = 0.048\) and \(t=30.\) Substituting those values into the PMT formula and calculating, we find the monthly payment is \[PMT =\frac{132,650\left(\frac{0.048}{12}\right)}{\left[1-\left(1+\frac{0.048}{12}\right)^{(-360)}\right]}\approx 695.97\nonumber \]
His mortgage payment is $695.97.
Paulo has a 20-year mortgage of $153,899 with an interest rate of 4.21%. Find Paulo’s monthly payment.
- Answer
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$949.72
The Gill family is buying a $250,000 house with a 10% down payment. If the loan is financed over 30 years at an interest rate of 4.8%, what is the monthly payment?
Solution
Down payment = 10% of $250,000 \(= 0.1\times \$250,000 = \$25,000\). Thus, the loan principal, \(P = \$250,000-\$25,000 = \$225,000\).
\[PMT =\frac{225,000\left(\frac{0.048}{12}\right)}{\left[1-\left(1+\frac{0.048}{12}\right)^{(-360)}\right]}\approx \$1,180.50\nonumber \]
The monthly payment is $1,180.50.
Find the monthly payment for the house in the above problem if the loan was amortized over 15 years.
- Answer
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$1,775.94
Total Mortgage Cost
To find the total amount of the payments over the life of the loan, multiply the monthly payment (PMT) by the total number of payments (=\(nt\)). This can be useful information, but not many people reach the end of their mortgage term - they tend to move before the mortgage is paid off.
The total paid, \(A\), on a \(t-\)year mortgage with monthly payment \(PMT\) is: \(A=PMT\times 12\times t\).
Cassandra buys a house with a 30-year mortgage of $99,596 at an APR of 5.35%. If she pays off the mortgage over the full 30 years, how much will she have paid in total?
- Solution
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To calculate the total paid over the life of the mortgage, we need to find the monthly payment first. Since \( P = $99,596, ~r = 0.0535\), and \(t = 30\), we have
\[ PMT=\frac{99,596\times\left(\frac{0.0535}{12}\right)}{\left[1-\left(1+\frac{0.0535}{12}\right)^{(-12\times 30)}\right]}\approx 556.16\nonumber\] The monthly payment is $556.16, and thus, the total of the payments over the loan term is
\[A= \$556.16\times 12\times 30 = \$200,217.60 \nonumber\] The total that Cassandra will pay for the mortgage is $200,217.60.
Arthur has a 15-year mortgage of $225,879 with an interest rate of 4.91%. If Arthur pays off the mortgage over the full 15 years, how much will he have paid in total?
- Answer
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$319,620.60
The total interest paid on a mortgage can be found by subtracting the principal from the total amount paid over the life of the loan.
The total interest on a mortgage is \(I=A-P\) where \(P\) is the mortgage’s starting principal and \(A\) is the total paid over the life of the mortgage.
Cassandra has a 30-year mortgage of $99,596 with an APR of 5.35%. How much interest will she pay over the life of the mortgage?
- Solution
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In Example \(\PageIndex{2}\), we found that the total Cassandra will pay for the mortgage is $200,217.60. Therefore, \(I=A-P=\$200,217.60−\$99,596=$100,621.60.\)
Arthur has a 15-year mortgage of $225,879 with an APR of 4.91%. How much interest will they pay over the life of the mortgage?
- Answer
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$93,741.60
Mr. Albers borrowed $425,000 from the bank for his new house at an interest rate of 4.7%. He will make equal monthly payments over the next 30 years. How much money will he end up paying the bank over the life of the loan, and how much of that will be interest?
- Answer
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The total of the payments is $793,519.20, and the interest paid for 30 years is $368,519.20
Mortgage Payoff
One of the most common problems involves finding the balance owed at a given time during the life of a loan. Suppose a person buys a house and amortizes the loan over 30 years but decides to sell the house a few years later. At the time of the sale, they are obligated to pay off their lender. Therefore, they need to know the balance still owed. Since most long-term loans are paid off early, this situation arises frequently.
To find the outstanding balance of a loan at a specific time, we need to determine the present value \(P\) of all future payments that have not yet been made. To calculate that balance, we use the installment loan payoff formula with \(n=12\). In this case, \(nt\) does not represent the total number of payments over the loan term. Instead, we use \(U\) for \(nt\), which represents the total number of remaining payments.
The payoff amount (\(P\)) for a mortgage is given by
\[P=\frac{PMT\left[1-\left(1+\frac{r}{12}\right)^{(-U)}\right]}{\left(\frac{r}{12}\right)} \nonumber \]
where \(PMT\) is the mortgage payment, \(r\) is the annual interest rate (APR), and \(U\) is the number of remaining (future) payments.
Note: Payments to lenders are always rounded up to the next penny. Do not round numbers during the computation, as rounding introduces errors. You may round only once at the end to report the final answer.
Mr. Jackson bought his house in 1995 and financed the loan for 30 years at an annual interest rate of 7.8%. His monthly payment was $1260. In 2015, Mr. Jackson decided to pay off the loan. Find the balance of the loan he still owes.
Solution
The reader should note that the original amount of the loan is not mentioned in the problem. This is because it is not needed to find the balance.
The original loan term was 30 years. Since 20 years have passed, there are 10 years remaining. Therefore, there are \(12 \times 10 = 120\) monthly payments left to be made on the loan.
As far as the bank or lender is concerned, Mr. Jackson is obligated to pay $1,260 each month for the next 10 years - a total of 120 remaining payments. However, since Mr. Jackson wants to pay off the loan now, we need to find the present value \(P\) at the time of repayment for the remaining 10 years of monthly payments of $1,260. Using the payoff formula, we find that Mr. Jackson needed to pay $104,761.34 to pay off the loan.
\[P=\frac{1,260\left[1-\left(1+\frac{0.078}{12}\right)^{(-120)}\right]}{\left(\frac{0.078}{12}\right)}\approx $104,761.34\nonumber \]
Mr. Nakahama bought his house in 1998. He financed his loan for 30 years at an interest rate of 6.2%, resulting in a monthly payment of $1,500. In 2015, 17 years later, he paid off the remaining balance of the loan. How much did he pay?
Solution
\(PMT = \$1,500, ~r=0.062, ~U=12\times(30-17)=156\). Therefore,
\[P=\frac{1,500\left[1-\left(1+\frac{0.062}{12}\right)^{(-156)}\right]}{\left(\frac{0.062}{12}\right)} \approx \$160,383.25\nonumber \]
He paid $160,383.25 to pay off the loan.
You want to purchase a home for $200,000 with a 30-year mortgage at an interest rate of 9.24%. Find (a) the monthly payment and (b) the balance owed after 20 years.
- Answer
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(a) $1,643.91 (b) $128,452.26
Escrow Payments
The last few examples have focused on mortgage payments, which cover the principal and interest. However, when you take out a mortgage, the total monthly payment is sometimes much higher. This is because your mortgage company may also require you to pay into an escrow account - a savings account maintained by the mortgage company.
Your insurance payments are set by your insurer, and the mortgage company will use funds from your escrow account to pay them on time. Your property taxes, which are typically a percentage of your home’s assessed value, are determined by the local government where you live. The assessed value is an estimate of your home’s value and does not necessarily reflect its purchase or resale price. Property taxes will also be paid by the mortgage company from your escrow account.
These escrow payments - which cover property taxes and insurance - can significantly increase your monthly mortgage payment beyond just the principal and interest.
Jenna decides to purchase a home with a mortgage of $108,450 at 6% interest for 30 years. The assessed value of her home is $75,600, and her property taxes amount to 5.7% of the assessed value. Jenna also has to pay home insurance every six months, which costs $744 per six-month period. How much, including escrow, will Jenna pay per month?
- Solution
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Using the PMT formula with = $108,405, = 0.06, and = 30, her monthly mortgage payment is
\[ PMT=\frac{108,450\times\left(\frac{0.06}{12}\right)}{\left[1-\left(1+\frac{0.06}{12}\right)^{(-12\times 30)}\right]}\approx \$649.95\nonumber\]
Jenna also pays into escrow 1/12 of her property taxes each month. Her property taxes are 5.7% of the assessed value of $75,600, which comes to 0.057 × $75,600 = $4,309.20 annually. Since this is an annual tax, she pays 1/12 of that amount each month, which equals $359.10. Jenna’s home insurance costs $744 every six months, so each month she pays $124.00 for insurance. Adding these together, her total monthly payment is $649.95 (for the principal and interest) + $359.10 (for property taxes) + $124.00 (for insurance) = $1,133.05. This is quite a bit more than the $649.95 for the principal and interest alone.
Destiny decides to purchase a home with a mortgage of $159,195.50 at 5.75% interest for 30 years. The assessed value of her home is $100,000, and her property taxes amount to 5.42% of the assessed value. Destiny also has to pay her home insurance every six months, which costs $843 per six-month period. How much, including escrow, will Destiny pay per month?
- Answer
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$1,521.20
Check Your Understanding
- Does renting or buying have tax advantages?
- Which has more restrictions, renting or buying?
- Which has housing cost that does not change?
- What is the name given to a loan for a home?
- What are the monthly payments for a 30-year mortgage of $108,993 with 6.14% interest.
- What is the cost of financing for a 30-year mortgage of $108,993 with 6.14% interest if the mortgage is paid off?
- What is the name of the account that the mortgage company holds your taxes and insurance in?
- Display Answers
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- Buying
- Renting
- Buying
- Mortgage
- $663.32
- $129,802.20
- Escrow
Exercises
I. In the following exercises, indicate if the advantage listed is for renting or buying a home.
- Short-term commitment.
- Tax advantage.
- Freedom to remodel.
- Builds equity.
- Cost is lower.
- You do not pay for repairs.
- No pet restrictions
- More flexibility to move.
- Housing cost is fixed.
- May have other amenities.
II. In the following exercises, find the mortgage payment for the given loan amount, interest rate, and term.
- Loan amount is $78,560, interest rate is 5.87%, 30-year mortgage.
- Loan amount is $125,800, interest rate is 6.5%, 30-year mortgage.
- Loan amount is $96,400, interest rate is 4.9%, 15-year mortgage.
- Loan amount is $267,450, interest rate is 5.25%, 20-year mortgage.
III. In the following exercises, find the total paid on the mortgage if it is fully paid through the term.
- Loan amount is $78,560, interest rate is 5.87%, 30-year mortgage.
- Loan amount is $125,800, interest rate is 6.5%, 30-year mortgage.
- Loan amount is $96,400, interest rate is 4.9%, 15-year mortgage.
- Loan amount is $267,450, interest rate is 5.25%, 20-year mortgage.
IV. In the following exercises, find the cost of financing for the mortgages if they are fully paid.
- Loan amount is $78,560, interest rate is 5.87%, 30-year mortgage.
- Loan amount is $125,800, interest rate is 6.5%, 30-year mortgage.
- Loan amount is $96,400, interest rate is 4.9%, 15-year mortgage.
- Loan amount is $267,450, interest rate is 5.25%, 20-year mortgage.
V. In the following exercises, find the total monthly payment, including both the mortgage payment and the escrow payment.
- Mortgage of $87,690 at 6.2% interest for 30 years. The assessed value of the home is $75,600. Property taxes come to 5.65% of assessed value. Home insurance of $815 is paid every six months.
- Mortgage of $143,900 at 5.05% interest for 30 years. The assessed value of the home is $90,150. Property taxes come to 5.88% of assessed value. Home insurance of $924 is paid every six months.
- Mortgage of $65,175 at 6.48% interest for 30 years. The assessed value of the home is $62,800. Property taxes come to 6.75% of assessed value. Home insurance of $558 is paid every six months.
- Mortgage of $245,950 at 5.35% interest for 30 years. The assessed value of the home is $156,500. Property taxes come to 6.41% of assessed value. Home insurance of $972 is paid every six months.
VI. For the following exercises, read the following: 15-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.
- The 15-year mortgage interest rate is 5.65%; (a) Find the payment, (b) Determine the total that would be paid if the mortgage was completed, and (c) Find the cost of financing for this mortgage.
- The 30-year mortgage rate is 6.4%; (a) Find the payment, (b) Determine the total that would be paid if the mortgage was completed, and (c) Find the cost of financing for this mortgage.
- How different are the payments, the total paid, and the cost to finance? Summarize your answer.
VII. For the following exercises, read the following: 15-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.
- The 15-year mortgage interest rate is 5.6%. (a) Find the payment, (b) Determine the total that would be paid if the mortgage was completed, and (c) Find the cost of financing for this mortgage.
- The 30-year mortgage rate is 6.25%. (a) Find the payment, (b) Determine the total that would be paid if the mortgage was completed, and (c) Find the cost of financing for this mortgage.
- How different are the payments, the total paid, and the cost to finance? Summarize your answer.