Buying a House with a MortgageCollege MathematicsSection 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 interest rate for the duration of the

loan

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

price0.15 249,000Down payment 37,350Down payment

Patty and Marshall must come up with a $37,350.00 down payment

B. Determine mortgage Mortgage = Selling price – down

payment249,000 37,350Mortgage 211,650Mortgage

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

Two points will cost them $4,233 at closing.

2 0.02 211,650points

2 4,233points

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) Determine adjusted monthly income by

subtracting from the gross monthly income any fixed monthly payments with more than 10 months remaining.

2) 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) Determine monthly principal and interest

payments using table 11.4. This gives you the amount of principal and interest per $1000 dollars of mortgage.

2) 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 - 45AMI = 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 borrowedPrincipal and Interest payment = x table value

1000

211,650P and I payment = x 6.65

1000P and I payment = 1,407.47

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

360

506,689.20

x

Principal and Interest Payment

Months in 30 years

Total Principal and Interest

Down Payment

Points

Total Cost of House Over 30 Years

37,350.004,233.00

$548,272.20

B. How much of the total cost is interest? Interest = Total cost of house – selling

price548,272.20 249,000Interest 299,272.20Interest

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

I PRT(211,650)(0.07)(1/12)I $1,234.63I

Interest

1,407.47 1,234.63 172.84Principal Payment 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.