Buying a House
with a
Mortgage
College Mathematics
Section 11.5
Objective:
The students will compute the necessary
information in buying a home with a
mortgage.
Homeowner’s Mortgage:
 long-term
loan (from a bank) in which a
property is pledged as security for
payment of the difference between the
down payment and sale price

Mortgage states the terms of the loan:
payment schedule, duration of the loan,
whether the loan can be assumed by
another party, and the penalty if payments
are late.
Down payment:
 amount
of cash the buyer must pay to the
seller before the lending institution will
grant the buyer a mortgage (could be 5%
to 50% of the purchase price)
Conventional Loan:
 fixed
loan
interest rate for the duration of the
Adjustable-Rate Loan:
 interest
rate for the variable-rate loan
may change every period, as specified in
the loan
Closing:
 the
final step in the sale process
Points:
 interest
prepaid by the buyer that may be
used to reduce the stated interest rate
the lender charges. One point is equal to
1% of the loan amount.
Example 1:
 Patty
and Marshall 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 down payment
 Down
payment = 15% of selling price
Down payment  0.15 249, 000
Down payment  37,350

Patty and Marshall must come up with a
$37,350.00 down payment
B. Determine mortgage
 Mortgage
= Selling price – down payment
Mortgage  249, 000  37,350
Mortgage  211, 650
 Their
mortgage (loan amount) will be for
$211,650.
C. Determine cost of 2 points
 Every
point is equal to 1% of the mortgage
amount
 2 points = 2% x mortgage amount
2 points  0.02 211, 650
2 points  4, 233
 Two
points will cost them $4,233 at closing.
Summary:
 At
closing, Patty and Marshall will have to
pay $37,350 as a down payment and
$4,233 for their 2 points. They should walk
in with $41,583.
What can you afford to pay?
 Banks
use a formula to determine the maximum
monthly payment that they believe is within the
purchaser’s ability to pay.
1)
2)
Determine adjusted monthly income by
subtracting from the gross monthly income any
fixed monthly payments with more than 10
months remaining.
Multiply the adjusted monthly income by 28%.
This amount is the maximum the purchaser can
afford to pay for principal, interest, property
taxes, and insurance combined.
What’s the mortgage payment?
 To
determine the total monthly mortgage
payment, do the following:
1)
2)
Determine monthly principal and interest
payments using table 11.4. This gives you the
amount of principal and interest per $1000 dollars
of mortgage.
Add property taxes and homeowners insurance
to principal and interest payment
Table 11.5 (Principal and
interest payment):
Number
of
Years
Rate%
10
15
20
25
30
4.0
$10.12
$7.40
$6.06
$5.28
$4.77
4.5
10.36
7.65
6.33
5.56
5.07
5.0
10.61
7.91
6.60
5.85
5.37
5.5
10.85
8.17
6.88
6.14
5.68
6.0
11.10
8.44
7.16
6.44
6.00
6.5
11.35
8.71
7.46
6.75
6.32
7.0
11.61
8.99
7.75
7.07
6.65
Example 2:


Suppose the Patty and Marshall’s gross income is $7250 and
they have…
 23 more monthly payments of $225 on their car loan
 17 more monthly payments of $175 on their kid’s braces
 11 more monthly payments of $45 on a furniture loan
 A monthly property tax bill of $165 for the new house
 A monthly home insurance bill of $115 for the new house
The bank will approve the loan if the total monthly payment
of principal, interest, property taxes, and homeowners’
insurance is less than or equal to 28% of their adjusted
monthly income.
B. What would this house cost?
 $211,650
mortgage
 30-year
 7%
interest rate
 Taxes are $165/month
 Insurance is $115/month
A. What’s 28% of their AMI?
 AMI
= gross income – bills(with more than
10 monthly payments remaining)
AMI = 7250 - 225 - 175 - 45
AMI = 6,805
28% of AMI = 0.28 6,805 = 1,905.40
 According
to the bank formula, Patty and
Marshall can afford to spend $1905.40 a
month on principal, interest, taxes and
insurance.

Using the table we find that a loan for 30 years at 7%
interest is going to cost them $6.65 per $1000 they
borrow. So….
amount borrowed
Principal and Interest payment =
x table value
1000
211,650
P and I payment =
x 6.65 P and I payment = 1,407.47
1000
Mortgage Payment = P and I + taxes + insurance
Mortgage payment = 1,407.47 + 165.00 + 115.00 = 1,687.47
 Given
these figures, the monthly mortgage
payment would be $1,687.47
C. Can they afford it?
 According
to the bank formula, they had
to find a house that would cost $1,905.40
or less a month. This house would only
cost them $1,687.47 a month. Since this is
below the 28% allowed, they would
qualify to purchase the house.
Example 3:
 Patty
and Marshall purchased a house
selling for $249,000. They made a 15%
down payment of $37,350 and obtained
a 30-year conventional mortgage for
$211,650 at 7%. They also paid 2 points
(prepaid interest) at closing. The monthly
principal and interest payment on their
mortgage is $1407.47.
A. What will this $249,000
house cost over 30 years?
1407.47
x 360
506, 689.20
37,350.00
 4, 233.00
$548, 272.20
Principal and Interest Payment
Months in 30 years
Total Principal and Interest
Down Payment
Points
Total Cost of House Over 30 Years
B. How much of the total cost
is interest?
 Interest
= Total cost of house – selling price
Interest  548, 272.20  249, 000
Interest  299, 272.20
 Total
interest paid is $299,272.00
C. How much of the first payment
is applied to the principal?


Remember, bank pays itself FIRST!!!!
Principal payment = monthly payment - interest
Interest
I  PRT
I  (211, 650)(0.07)(1/12)
I  $1, 234.63
Principal Payment  1, 407.47  1, 234.63  172.84

Of the $1407.47 payment that is made on the
first month, only $172.84 goes toward paying
down the $211,650 you owe the bank.