Buying a House with a Mortgage College Mathematics Section 11.5.
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Transcript of Buying a House with a Mortgage College Mathematics Section 11.5.
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Buying a House with a MortgageCollege MathematicsSection 11.5
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Objective: The students will compute the necessary information in buying a home with a mortgage.
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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.
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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)
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Conventional Loan: fixed interest rate for the duration of the
loan
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Adjustable-Rate Loan: interest rate for the variable-rate loan
may change every period, as specified in the loan
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Closing: the final step in the sale process
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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.
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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.
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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
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B. Determine mortgage Mortgage = Selling price – down
payment249,000 37,350Mortgage 211,650Mortgage
Their mortgage (loan amount) will be for $211,650.
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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
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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.
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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.
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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
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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
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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.
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B. What would this house cost?
$211,650 mortgage 30-year 7% interest rate Taxes are $165/month Insurance is $115/month
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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.
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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
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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.
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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.
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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
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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
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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.