# Buying a House with a Mortgage College Mathematics Section 11.5.

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

B. Determine mortgage  Mortgage = Selling price – down payment  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.

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): NumberofYears Rate%1015202530 4.0\$10.12\$7.40\$6.06\$5.28\$4.77 4.510.367.656.335.565.07 5.010.617.916.605.855.37 5.510.858.176.886.145.68 6.011.108.447.166.446.00 6.511.358.717.466.756.32 7.011.618.997.757.076.65

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)  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….  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? 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  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  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.