1. Buying a House with a Mortgage
Section 10.5
Buying a House with a Mortgage

2. What You Will Learn
Upon completion of this section, you will be able to:
Solve problems involving conventional mortgages.
Solve problems involving adjustable-rate mortgages.

3. Homeowner’s Mortgage
A homeowner’s mortgage is a long-term loan in which the property is pledged as security for 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, whereas 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
The Martins 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 × $211,650 = $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.
Generally, an ARM rate is fixed for an initial period of time, called the initial rate period. Thereafter, the rate may go up or down based on movements in the interest rate market.

20. Adjustable Rate Mortgages
Most ARMs have an initial rate period of 5 or 7 years.
The initial rate is usually lower than the rate for conventional mortgages, thus making the loan attractive to buyers.
After the initial rate period, the rate may rise and cause the monthly mortgage payments to also rise.
Typically, after the initial rate period, the ARM rate is adjusted once a year.

21. Example 5: An Adjustable-Rate Mortgage
The Ghiselins purchased a condominium for $275,000 with a down payment of $115,000. They obtained a 15-year adjustable rate mortgage with the following terms. The interest rate is based on the one-year Treasury bill rate, which currently is 0.5%, and the add-on rate, which is 3.0%. The initial rate period is 5 years, and thereafter the interest rate is adjusted one a year and a new monthly mortgage payment is calculated.

22. Example 5: An Adjustable-Rate Mortgage
a) Determine the Ghiselins’ initial ARM rate.
Solution
a) The ARM rate is the sum of the one-year Treasury bill rate, 0.5%, and the add-on rate, 3.0%. Thus, the initial ARM rate is % + 3.0%, or 3.5%.

23. Example 5: An Adjustable-Rate Mortgage
b) Determine the Ghiselins’ initial monthly payment for principal and interest.
Solution
b) Use table 10.4 on the following slide.
The amount of the loan is $275,000 − $115,000, or $160,000. Divide the amount of the loan by $1000 to get 160. Now looking at the table with r = 3.5% for 15 years, we find the value of

24. Example 5: An Adjustable-Rate Mortgage

25. Example 5: An Adjustable-Rate Mortgage
Solution
Thus, the initial monthly payment for principal and interest is $

26. Example 5: An Adjustable-Rate Mortgage
c) If, after the 5-year initial rate period, the rate of the one-year Treasury bill rises to 1.5%, determine the Ghiselins’ new ARM rate.
Solution
The sum of the new one-year Treasury bill rate, 1.5%, and the add-on rate, 3.0%, is 4.5%. Thus, the Ghiselins’ new ARM rate is 4.5%.

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
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.
An aggregate rate cap limits the interest rate increase and decrease over the entire life of the loan.

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