1. Buying a House with a Mortgage
Section 10.5
Buying a House with a Mortgage
Learning about the costs of obtaining a mortgage can help you make wise decisions if you choose to purchase a home.

2. Homeowner’s Mortgage
A homeowner’s mortgage is a long-term loan in which the property is pledged as security for payment of the difference between the down payment and the sale price.
Two most popular types of mortgages:
Conventional loan: Interest rate is fixed for the duration of the loan.
Adjustable-rate loan (variable-rate loan): Interest rate may change every period, as specified in the loan.
Closing costs are also paid when purchasing a home and some will pay points (interest prepaid by the buyer and may be used to reduce the stated interest rate the lender charges). One point is equal to 1% of the loan amount.

3. Qualifying for a Mortgage
Banks first need to determine the buyer’s adjusted monthly income by subtracting from the gross monthly income any fixed monthly payments (student loan, car loan, etc.…) with more than 10 months remaining. Then they multiply the adjusted monthly income by 28% which will give the maximum monthly house payment the bank believes that the buyer can afford. This includes: principal, interest, property tax, insurance.

4. Example 1: Down Payment and Points
The Martins wish to purchase a house selling for $249,000. They plan to obtain a loan from their bank. The bank requires a 15% down payment, payable to the seller, and a payment of 2 points, payable to the bank, at the time of closing.
a) Determine the Martin’s down payment.
The down payment is 15% of $249,000
0.15 × $249,000 = $37,350.
b) Determine the amount of the Martin’s mortgage. [Will need later]
The mortgage on the Martin’s new home is the selling price
minus the down payment.
$249,000 – $37,350 = $211,650.
c) Determine the cost of the 2 points paid by the Martins on their mortgage.
2 points is 2% of the mortgage.
0.02 × $211,650 = $4233
At the closing, the Martins will pay the down payment of $37,350 to the seller and the 2 points, or $4233, to the bank.

5. Principal and Interest Payment Formula
m is principal and interest payment
p is the amount of the mortgage
r is the interest rate as a decimal
n is the number of payments per year
t is the time in years

6. Principal and Interest Payment Formula Practice
m is principal and interest payment
p is the amount of the mortgage
r is the interest rate as a decimal
n is the number of payments per year
t is the time in years
Determine the monthly principal and interest payment for a 20-year mortgage when the amount financed is ​$255,000 and the annual percentage rate​ (APR) is 4.0%. Round to the nearest cent as needed.
The monthly principal and interest payment is ​$1,

7. Example 1: Continuation
Suppose the Martins’ gross monthly income is $7250 and they have 23 remaining monthly payments of $225 on their car loan, 17 remaining payments monthly of $175 on their daughter’s braces, and 11 monthly payments of $45 on a loan for furniture. The property taxes and homeowners’ insurance on the house they plan to buy are $165 and $115 per month. Their bank will approve a loan that has a total monthly mortgage payment that is less than or equal to 28% of their adjusted monthly income.
Determine 28% of their adjusted monthly income.
Subtract the sum of their monthly payments from their gross monthly income.
$225 + $175 + $45 = $445
$7250-$445 = $6,805
Take 28% of the adjusted monthly income.
.28 x $6,805 = $
Martins’ adjusted monthly income is $

8. Example 1: Continuation
Suppose the Martins’ gross monthly income is $7250 and they have 23 remaining monthly payments of $225 on their car loan, 17 remaining payments monthly of $175 on their daughter’s braces, and 11 monthly payments of $45 on a loan for furniture. The property taxes and homeowners’ insurance on the house they plan to buy are $165 and $115 per month. Their bank will approve a loan that has a total monthly mortgage payment that is less than or equal to 28% of their adjusted monthly income.
They want a 30-year, $211,650 mortgage. If the interest rate is 7%, determine the total monthly mortgage payment (including principal, interest, property taxes, and homeworkers’ insurance.
p = $211,650, r = 0.07, n =12, t = 30
p = , r = , n = , t = $
$ $165 + $115 = $
Martins’ total monthly mortgage payment is $

9. Example 1: Continuation
Suppose the Martins’ gross monthly income is $7250 and they have 23 remaining monthly payments of $225 on their car loan, 17 remaining payments monthly of $175 on their daughter’s braces, and 11 monthly payments of $45 on a loan for furniture. The property taxes and homeowners’ insurance on the house they plan to buy are $165 and $115 per month. Their bank will approve a loan that has a total monthly mortgage payment that is less than or equal to 28% of their adjusted monthly income.
Do they qualify for this mortgage?
28% of the Martins’ adjusted monthly income is $
Martins’ total monthly mortgage payment is $
Yes, The Martins qualify for this mortgage.

10. Example 2: Total Cost of a House
The Martins’ purchased a house selling for $249,000 with 15% down payment of $37,350 and obtained a 30-year conventional mortgage for $211,650 at 7%. They also paid 2 points at closing. Their monthly principal and interest payment of their mortgage is $ Recall points are considered prepaid interest.
Determine the total amount, including principal, interest, down payment, and points, they will pay for their house over 30 years.
x 360 (30 years x 12 months per year) 30x12 = 360 payments
$506,919.60
+ 37, down payment
+ 4, points (211,650 x .02) = 4233
$548, Total cost of the house.
(might not be exact – Final mortgage payment slightly more or less)

11. Example 2: Total Cost of a House
The Martins’ purchased the house selling for $249,000 with 15% down payment of $37,350 and obtained a 30-year mortgage for $211,650 at 7%. They also paid 2 points at closing. Their monthly principal and interest payment of their mortgage is $ Recall points are considered prepaid interest.
How much of the cost in part(a) is interest?
$548, Total cost of the house.
-249, Purchase Price
$299, Total interest (including the 2 points)
How much of the first mortgage payment is applied to the principal?
Subtract the amount of interest on the first payment from the
monthly principal and interest payment.
Use simple interest formula I = prt
I = $211,650 x .07x 1/12
= $
$ Monthly principal and interest payment
Interest paid for the first month
$ Principal paid for the first month.
Balance due on load after the fist monthly payment is $211, = 211,476.52

12. Amortization Schedule
By repeatedly using the simple interest formula month to month on the unpaid balance, you could calculate the principal and the interest for all the payments, which is a tedious task.
However, a list containing the payment number, payment on the interest, payment on the principal, and balance of the loan can be prepared using a computer. Such a list is called a loan amortization schedule.

13. Amortization Schedule

14. Other Types of Mortgages
ARMs or variable-rate mortgages.
FHA Mortgage
VA Mortgage
Graduated Payment Mortgage (GPM)
Balloon-Payment Mortgage (BPM)
Home Equity Loans
Also, see

15. Installment Payment Formula
m is installment payment
p is the amount financed
r is the annual percentage rate as a decimal
n is the number of payments per year
t is the time in years