Question: Taxes and home insurance add to $3,000. Interest rates on a 15year mortgage and a
30year 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 interestrate/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 interestrate/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 15year FRM and the 30year 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 15year 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 15year FRM ranges
from $94,320 to $100,273.
The house payment for the 30year FRM ranges from $1,726 to
$1,907.
Required household income ranges from $69,033 to $76,264.
A previous post revealed that 15year FRMs tend to increase
wealth and reduce risk.
However, this post reveals that many individuals cannot
afford the payments on a 15year FRM.
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