The cost of 0.125 percentage
points
A recent CNBC article
suggests that mortgage interest rates are a more important determinant of the
home purchase decision than house prices.
A quote from the article:
"It never ceases to amaze me how hung up mortgage borrowers
can be on rate," said Matthew Graham of Mortgage News Daily. "In
fact, a lot of times we have to remind them that the .125 percent difference in
rate only amounts to X dollars and they're surprised."
Some Comments:
The issue of a 0.125 percent difference in rates is a red
herring that is not applicable for many real world situations because often
differences among options are much larger than 0.125.
Rate differentials due to FICO score problems are much larger
than 0.125.
When rates fall the ability to refinance is crucial. A marginal borrower that gets a slightly
higher rate may pay much more over the life of the loan because of her
inability to refinance.
The rate difference across mortgage types is huge right
now. A borrower capable of using a 7/23
ARM or a 15year FRM might have an interest rate more than 1 full percentage
point lower than the 30year FRM.
Still it is worth analyzing the lifetime loan costs attributable
to a 0.125 percentage point difference in interest rates.
There are two components to the lifetime cost differential
stemming from the 0.125 percentage points.
The first component involves the lower monthly mortgage payment. The second component involves differences in
the rate at which the mortgage is paid down.
The total value of the cost savings from the lower mortgage
interest rate also depends on the length of time the person holds the mortgage.
Questions: What is the difference between a 0.125
percentage point difference in mortgage rates on mortgage payment and the pay
down of the mortgage balance over a 5, 10, 15, 20, 25 and 30 year period for a
30year mortgage with 4.0% interest rate and a 4.125% interest rate? What is the future value of both the lower
mortgage payment and the faster equity build up under the two interest rate
assumptions?
Assume a $500,000 mortgage.
Calculations:
The monthly mortgage payment
on the 4.0% loan and the 4.125% loan are calculated directly from the PMT
function. The difference summarized
below is $36 per month.
Rate

0.04

0.04125

0.00125

Period

360

360

0

PV

500000

500000

0

FV

0

0

0

TYPE

0

0

0

Mortgage Payment

$2,387

$2,423

$36

The mortgage balance reduces
faster at the lower interest rate.
However, by definition after 30 years both 30year FRMs have a $0
balance.
The mortgage balance
reduction calculation is obtained by plugging rate, number of payments, payment
amount, PV of the loan and loan type into the payment function. PMT is calculated above and other parameters
are given in the problem.
Impact of the 0.125
percentage points on loan balances


Loan Balance After 5
Years

$452,238

$453,144

$907

Loan Balance After 10
Years

$393,920

$395,576

$1,656

Loan Balance After 15
Years

$322,714

$324,846

$2,132

Loan Balance After 20
Years

$235,772

$237,946

$2,174

Loan Balance After 25
Years

$129,616

$131,178

$1,562

Loan Balance After 30
Years

$0

$0

$0

The loan balance impact is
not large for this 30year FRM problem.
It is a bit over $2,000 for a borrower who holds the property for 15
years.
$36 per month does not sound
like much but the mortgage is for 30 years.
The future value of the monthly payment differential also includes
interest.
FV of Mortgage Payment
Differential


Years

FV @ 4%

FV @ 4.125%

5

$2,398

$2,406

10

$5,326

$5,362

15

$8,902

$8,993

20

$13,267

$13,455

25

$18,597

$18,937

30

$25,105

$25,672

Most people hold their
mortgage for around 7 years so for the typical mortgage holder we are talking
about $4,000 on a $500,000 loan.
However, the person who holds
the mortgage for 30 full years will pay around $26,000 more on the loan because
of the 0.125 percentage points.
Concluding Thoughts: Is the 0.125 percentage point
the actual excess interest rate on your loan.
If so, the penalty is small.
However, you may be able to save far more than 0.125 percentage points
by waiting a bit and reducing your FICO prior to purchasing your house.
As I said above, the CNBC
quote is a bit of a red herring. Rates
are more important than depicted by this problem because the spread among
alternatives can be very large and issues like the ability to refinance are
also important.
Related Issue: One of the issues where rates matter a lot
involves the mortgage term decision. The
term structure of mortgage rates remains fairly steep in that the 30year FRM
remains substantially higher than the 15year FRM. A 15year FRM (even at a lower interest rate)
entails higher payments but the 15year FRM is still probably for most of us
the best investment out there.
I wrote this post on the mortgage term decision in 2013 but the term structure is still steep and this post is still relevant today.
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