1. Section 11.5 Buying a House with a Mortgage

2. What You Will Learn Homeowner’s Mortgage Conventional Loans
Adjustable-Rate Mortgages

3. Homeowner’s Mortgage
A homeowner’s mortgage is a long-term loan in which the property is pledged as a security payment of the difference between the down payment and the sale price.

4. Homeowner’s Mortgage
The two types are the conventional loan and the adjustable-rate loan (or the variable-rate loan).
The major difference between the two is that the interest rate for a conventional loan is fixed for the duration of the loan, where as the interest rate for the variable-rate loan may change every period, as specified in the loan.

5. Homeowner’s Mortgage
Lending institutions may require the buyer to pay one or more points for a loan at the time of the closing (the final step in the sale process). According to the Internal Revenue Service, points are 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.

6. Example 1: Down Payment and Points
Patricia and Marshall Martin 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.

7. Example 1: Down Payment and Points
a) Determine the Martin’s down payment.
Solution
The down payment is 15% of $249,000 or
0.15 × $249,000 = $37,350.

8. Example 1: Down Payment and Points
b) Determine the amount of the Martin’s mortgage.
Solution
The mortgage on the Martin’s new home is the selling price minus the down payment.
$249,000 – $37,350 = $211,650.

9. Example 1: Down Payment and Points
c) Determine the cost of the 2 points paid by the Martins on their mortgage.
Solution
2 points is 2% of the mortgage.
0.02 × $249,000 = $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.

10. Qualifying for a Mortgage
Banks use a formula to determine the maximum monthly payment that they believe is within the purchaser’s ability to pay.
They calculate the adjusted monthly income which equals the gross monthly income minus any fixed monthly payments (with more than 10 payments remaining).

11. Qualifying for a Mortgage
They multiply that result by 28%.
This is the maximum monthly payment the lending institution believes the purchaser can afford.
This includes: principal, interest, tax, insurance.

12. 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

13. Example 3: Using the Principal and Interest Payment Formula
Use the principal and interest payment formula to calculate the Martin’s monthly principal and interest payment. Recall that the Martins are seeking a 30-year, $211,650 mortgage with an interest rate of 7%.

14. Example 3: Using the Principal and Interest Payment Formula
Solution
p = $211,650, r = 0.07, n =12, t = 30

15. Example 3: Using the Principal and Interest Payment Formula
Solution

16. Example 3: Using the Principal and Interest Payment Formula
Solution
Thus, the Martins’ monthly principal and interest payment is $

17. 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.

18. Amortization Schedule

19. Adjustable Rate Mortgages
Also, called ARMs or variable-rate mortgages.
The monthly mortgage payment rate remains the same for a 1, 2, or 5-year period, even though the interest rate of a mortgage may change every 3 or 6 months or some other predetermined period.

20. Adjustable Rate Mortgages
The monthly payment is readjusted after the time period so the loan will be paid off in the set amount of time or the bank may extend the time period of the loan beyond the predetermined years to make the payment affordable.

21. Example 5: An Adjustable-Rate Mortgage
Tony and Keisha Torrence purchased a house for $115,000 with a down payment of $23,100. They obtained a 30-year adjustable-rate mortgage with the following terms. The interest rate is based on a 6-month Treasury bill. The interest rate charged is 3% above the interest rate of the 6-month Treasury bill (3% is the add on rate).

22. Example 5: An Adjustable-Rate Mortgage
The interest rate is adjusted every 6 months on the date of adjustment. The interest rate will not change more than 1% (up or down) when it is adjusted. The maximum interest rate for the duration of the loan is 12%. There is no lower limit on the interest rate. The initial mortgage interest rate is 5.5%, and the monthly payments (including

23. Example 5: An Adjustable-Rate Mortgage
principal and interest) are adjusted every 5 years.
a) Determine the initial monthly payment.
Solution
Divide the amount of the loan, $115,000 – $23,100 = $91,900, by $1000, to get Multiply by the value from Table 11.4, r = 5.5%, 30 yr

24. Table 11.4

25. Example 5: An Adjustable-Rate Mortgage
Solution
$ × 91.9 ≈ $521.80
Thus, the initial monthly payment for principal and interest is $
This amount will not change for the first 5 years of the mortgage.

26. Example 5: An Adjustable-Rate Mortgage
b) Determine the adjusted interest rate in 6 months if the interest rate on the Treasury bill at that time is 2%.
Solution
The adjusted interest rate in 6 months will be the Treasury bill rate plus the add on rate.
2% + 3% = 5%

27. Rate Caps
To prevent rapid increases in interest rates, some banks have a rate cap. A rate cap limits the maximum amount the interest rate may change.
A periodic rate cap limits the amount the interest rate may increase in any one period.

28. Rate Caps
An aggregate rate cap limits the interest rate increase and decrease over the entire life of the loan.
A payment cap limits the amount the monthly payment may change but does not limit changes in interest rates.

29. Other Types of Mortgages
FHA Mortgage
VA Mortgage
Graduated Payment Mortgage (GPM)
Balloon-Payment Mortgage (BPM)
Home Equity Loans
Also, see