Math For The Liberal Arts Project 2

A Case Study of Paying Extra Principal on a Mortgage

Great Idea or ‘Height of Foolishness’? Activity Sheet

Before you begin: Review the loan basics in unit 4D of your textbook regarding the payment formula and the roles that interest and principal play in an amortization. Then carefully read the following pieces of advice written by two different nationally syndicated financial columnists (Sharon Epperson and Bruce Williams) regarding paying extra principal on a mortgage: • Sharon Epperson from MoneySmart of USAWeekend.com

Pay mortgage early? Q: My husband and I are 49 and 48 and are paying extra on our mortgage to have it paid off by the time we're 56. My friend says that will hurt us on our taxes; my husband says it's better to save the money in interest now than to worry about a mortgage tax deduction later. What's your take? �S.R. Sheboygan, Wis.

A: You married a smart man. Paying off your mortgage early will save thousands of dollars, and you'll get a reliable rate of return on your investment (you save the interest you would have paid on your mortgage). Yes, you'll lose the mortgage interest tax deduction when that happens. But if you're in the 25% tax bracket, for example, you'd only get back a quarter for each $1 in interest you pay -- not such a big break. If you're debt-free and maxing out your 401(k) and IRAs, which offer tax breaks, paying up early isn't a bad idea. Source: http://www.usaweekend.com/08_issues/080511/080511thinksmart-mortgage-broadway- tickets.html (Posted May 11, 2008).

• Bruce Williams from Smart Money 
 DEAR
BRUCE:
I
have
a
friend
who
says
that
you
often
advise
that
it
is
not
wise
to
pay
off
a
 mortgage
in
advance.
Could
you
tell
me
in
one
paragraph
why
this
is
a
bad
idea?
It
seems
to
me
 that
being
debt‐free
is
a
goal
worth
working
toward.
–
L.H.,
Syracuse,
N.Y.
 
 DEAR
L.H.:
In
a
nutshell,
the
cheapest
money
that
you
can
borrow
is
against
a
first
mortgage
on
 your
primary
residence.
Generally
speaking,
it’s
in
a
sub‐7
percent
range
today.
It
is
not
too
 difficult
to
earn
substantially
more
than
that
in
the
marketplace,
so
why
pay
off
the
loan
early
 and
settle
for
an
effective
return
of
below
7
percent?
You
could
invest
this
money
elsewhere
at
a
 far
better
return.
In
addition,
if
you
itemize
the
interest
that
you
are
paying
on
the
home
loan,
it
 becomes
a
deductible
item.
To
me,
it’s
a
no‐brainer.
For
younger
people
to
pay
off
a
mortgage
 early
is,
in
my
opinion,
the
height
of
foolishness.
When
you
get
into
your
60s
and
the
idea
of
 having
your
home
paid
for
outdistances
the
need
for
return,
I
have
no
objection.
 Source: “Should
35‐year‐old
save
for
down
payment
or
retirement?"
Post
Register,
July
19,
2001.


Copyright © 2011 Pearson Education, Inc. Publishing as Addison-Wesley.

Download Spreadsheet: (for student)

• Download or ask your instructor for the file “Financial Toolboxes.xls” which provides you a collection of mini financial calculators and a worksheet on the role of the negative.

Procedure: In our brief case study, we assume the Thomas and Jefferson families have identical mortgages (30-year term, fixed-rate 6% APR, and a loan amount of $175,000). The Thomas family will not pay extra but the Jeffersons will. Follow the steps below prior to your analysis. 1. Using the Payment mini calculator of the Financial Toolboxes spreadsheet, calculate the

mortgage payment (the same for both families). Required Monthly Payment = $_________

2. Assume that the Thomas’s will make only the required mortgage payment. The Jeffersons, however, would like to pay off their loan early. They decide to make the equivalent of an extra payment each year by adding an extra 1/12 of the payment to the required amount. Complete the following calculations to find what they plan to pay each month: a. 1/12 of the required monthly payment = $_________

b. By adding this 1/12 to the required payments, the Jeffersons plan to pay $_________

each month.

3. The Thomas’s will take the full 30 years to pay off their loan, since they are making only the required payments. The Jefferson’s extra payment amount, on the other hand, will allow them to pay off their loan more rapidly. Use the Years mini financial calculator of the Financial Toolbox spreadsheet to calculate the approximate number of years (nearest 10th) it would take the Jeffersons to pay off their loan. Number of years to pay off loan = _______

Analysis: For the Thomas Family: assume that they could afford to make the same extra payment as the Jeffersons, but instead they decide to put that money (#2a. from Procedures above) into a savings plan called an annuity. Use the Future Value mini financial calculator of the Financial Toolbox spreadsheet to calculate how much they will have in their savings plan at the end of 30 years at the various interest rates. Write your answers (to the nearest dollar) in the appropriate cells of the table below. For the Jefferson Family: assume that they save nothing until their loan is paid off, but then after their debt is paid, they start putting their full monthly payment and 1/12 (#2b. from Procedures above) into a savings plan. The time in months they invest is equal to 360 months minus the number of months needed to pay off the loan (#3 from Procedures above) multiplied by 12. Use the Future Value mini financial calculator to calculate how much they will have in their savings plan at the various interest rates. Write your answers (to the nearest dollar) in the appropriate cells of the table below.

Copyright © 2011 Pearson Education, Inc. Publishing as Addison-Wesley.

Discussion: 1. What generalizations can you make from the annuity amounts reflected in the analysis table

above with regards to the different strategies taken by the families? That is, from a purely financial aspect of the calculations in your table what generalizations could you make regarding the two different strategies?

2. What assumptions may not necessarily be valid for a typical family regarding both the loan rate and savings plan rate?

3. Discuss (as directed by your instructor) some basic pros and cons to these two very different approaches the Thomas and Jefferson families made with their extra monthly payment. Consider various ideas such as possible changes in the family’s employment situation, market performance, tax deductions, etc.

4. Comment on the merits of the advice you read from the two financial columnists. 5. Note the dates of the advice columns. How might market performance figure in to their

advice they gave at that time? 6. Why do you think Sharon Epperson’s advice at the end specifically calls attention to an

assumption of whether you are “debt-free and maxing out your 401(k) and IRAs?” 7. If you were to pay extra principal on a mortgage, when is the best time to do it (early or later

in the loan process) and why? 8. When you pay extra principal on a loan, describe whether you feel you are actually earning

interest on that money or not. That is, how does the old adage “a penny saved is a penny earned” apply in this context?

9. [Bonus] Rework your calculations using a different starting interest rate for the mortgage and/or a different extra payment amount. Do these changes affect any of the generalizations you have made above? Explain.

Thomas Family Jefferson Family 1/12th of Monthly Payment ___________ Monthly Payment + Extra 1/12th ___________

Rates Annuity Amount in 360 Months: Rates Annuity Amount in _____ Months: 0% 0% 1% 1% 2% 2% 3% 3% 4% 4% 5% 5% 6% 6% 7% 7% 8% 8%

Copyright © 2011 Pearson Education, Inc. Publishing as Addison-Wesley.

Chapter 4D/Consumer Mathematics Project 4D Instructions - Spring 2016.pdf