## Thursday, March 20, 2014

### Interest rates, mortgage maturity, and qualifying for a mortgage.

Question:   Taxes and home insurance add to \$3,000.   Interest rates on a 15-year mortgage and a 30-year mortgage, initially 3.25% and 4.25%, increase to 4.25% and 5.25% respectively.

How does the increase in interest rates impact the house payments for the four interest-rate/mortgage combinations?

Assume that a condition for qualifying for a mortgage is that the house payment should not be greater than 30% of household income.   What income will qualify a person for a mortgage under the four interest-rate/mortgage combinations?

Answer:   The mortgage component of the house payment is obtained from the PMT function in Excel.   Simply plug in the appropriate values for rate, number of periods and the present value of the loan balance.  Also, the FV (loan balance at maturity) is \$0 and loan payments are made at the end of the month type=0.

The total monthly house payment includes monthly payments for real estate taxes and insurance.  (In this case, \$3,000/12.)

The annual household income needed to purchase the home is the monthly house payment multiplied by 12 divided by 0.30.   This follows from

APAY = 0.30 x HI

Where APAY is the annual payment and HI is household income.

Calculations for the house payments and the required annual household income for the 15-year FRM and the 30-year FRM under the two interest rate scenarios are presented in the table below.

 Potential House Payments for a \$300,000 Mortgage rate 0.0325 0.0425 0.0425 0.0525 nper 180 180 360 360 pv \$300,000 \$300,000 \$300,000 \$300,000 FV 0 0 0 0 type 0 0 0 0 Mortgage Payment (\$2,108) (\$2,257) (\$1,476) (\$1,657) Insurance and Taxes (\$250) (\$250) (\$250) (\$250) Total House Payment (\$2,358) (\$2,507) (\$1,726) (\$1,907) Required Household Annual Income \$94,320 \$100,273 \$69,033 \$76,264

Some Observations:

The house payment for the 15-year FRM ranges from \$2,108 at an interest rate of 3.25% to \$2,507 at an interest rate of 4.25%.

The required household income for the 15-year FRM ranges from \$94,320 to \$100,273.

The house payment for the 30-year FRM ranges from \$1,726 to \$1,907.

Required household income ranges from \$69,033 to \$76,264.

A previous post revealed that 15-year FRMs tend to increase wealth and reduce risk.

However, this post reveals that many individuals cannot afford the payments on a 15-year FRM.