Download Use of Algebra in Financial Mathematics

Dr. Amit Dave
Cornell Grant
Georgia Piedmont Technical College
Atlanta, Georgia
 Importance
of Financial Mathematics
 Many students have very limited knowledge
of personal finance.
 They tend to make decision without realizing
the impact of their decision on their personal
finance.
 Borrowing money for automobile, home,
education can be a big burden if not
managed properly.
A survey conducted in 2008 by the US
Department of Education reflects continued
increases in student debt.
 According to this survey, the average debt of a
public university student was about $17,000 in
2004, and it rose 24% to $23,200 in 2008.
 According to the US Department of Education,
the national two-year federal student loan
cohort default rate rose from 9.1 percent for FY
2010 to 10 percent for FY 2011 and three-year
cohort default rate rose from 13.4 percent for FY
2009 to 14.7 percent for FY 2010.

 The
average entry-level job pays $46,000 a
year, and average college senior graduates
with nearly $23,000 in debt.
 That’s about half of the first year salary and
not including other expenses like insurance,
rent, utilities, car payments, etc.
 These figures clearly emphasize the
importance of financial literacy among
students.
A
research study conducted by Sallie May
showed nearly 85% undergraduate students
expressed their desire to have a college
course to teach money management skills.
 Approximately 25% of high schools in the
United States teach personal finance.
 Average student debt for a graduating senior
in 2008 increased by 24% compared to 2004.
The average debt amount for graduate was
$23,200 compared to $18650 in 2004.
 In
2008, the average debt at a public
university was $20,200 - 20% higher than
2004.
 In 2008, the average debt at a private nonprofit university was $27,650 – 29% higher
than 2004.
 In 2008, the average debt at a private forprofit university was $33,050 – 23% higher
than 2004.
 Approximately 40-50% of the graduating kids
will have less that $10,000.00 of net worth
during their liftime.
 In
2008, 67% graduating students from a four
year college had student debt; which
equates to approximately 1.4 million
students (27% higher than 2004).
 62% graduates from public universities had
student loans
 72% graduates from private non-profit
universities had student loans
 92% graduates from private for-profit had
student loans compared to 85% of the
students in 2004.
Students do not know enough about personal
finance
 They start at a younger age
 There are greater temptations
 They have more debt options
 They have more debt in general
 Student loans are more expensive
 People are going bankrupt
 Students start saving later
 The government would not be able to support
them
 Not everyone is given the same chance

 Many
students enrolled in College Algebra
class will not take another math class or any
business class if it is not required in their
major of studies.
 Majority of these students are adult students
in their early to mid 20’s.
 They never received any formal training in
money management.
 These students need guidance from some
source and algebra course can be a
wonderful source.
College Algebra class does not include any
chapter that covers financial mathematics.
 Instructor must be creative in using algebraic
concepts to teach financial mathematics.
 Instructor is expected to be knowledgeable in
personal finance.
 Just about all financial mathematics calculations
can be performed using algebraic formula.
 The idea is to assist students to use algebraic
concepts to solve problems with financial
applications, which in turn helps students to
make best financial decisions.

 The
real world applications when
incorporated with technology can be great
motivator for students.
 Students are exposed to formulas to
determine monthly car payment, saving,
investment, and retirement planning.
 Students also work with examples on
mortgage, and debt.
 Difference
between simple interest and
compound interest.
 Explain the difference between regular IRA
(401K) and Roth IRA.
 Home loan calculations.
 Automobile loan and interest calculations.
 Resources for information on financial
planning.
 Students
do not know the difference
between simple and compound interest.
 The difference is explained with real world
example.
 Explain the magic of compounding.
 Explain the difference between APR and APY.
 Introduce them to continuous compounding.
 Majority
of the students do not know the
difference between regular IRA(401K) and
Roth IRA.
 The project involves creating a nest egg with
regular IRA and Roth IRA. For this purpose
the concept of exponent is used in the
classroom.
 Each student is assigned a fixed amount
(500.00) for investment per year for 25 years
at 8% interest rate.
 Students
are required to use the formula
FV = Future Value
PMT = Payment
i = Interest rate
 The
future value of the $500.00 invested
each year = $36,552.97.
 Interest earned = $36,552.97 - $12,500.00 =
$24052.97.
 Many students do not have any idea that a
small amount invested each year after year
could result in such a large amount.
 On top of this, the entire amount is tax free
since the Roth IRA is after tax investment.
 Same
calculation is performed for regular IRA
(401K); however since the regular IRA (401K)
is based on pre-tax dollars, the entire
amount ($36,552.97) is taxable. The tax rate
depends on the income of the individual.
 Students
are asked to stop investing $500.00
per year after 25 years and invest $36,552.97
for another 10 years at 6% interest
compounded annually.
 Compound interest formula is used to
calculate the future value.
FV = $65,460.80
 An
investment of $12,500 grew to $65,460.80
in 35 years.
 These examples helped students understand
the magic of compounding while working
with algebraic concepts.
 Students
are asked to estimate the amount
they need to save today so they can
withdraw a fixed amount every month, six
months, or year.
 The formula for Present Value of the Annuity
is used to perform this calculations.
 The
same formula is used to perform
calculations for “n”, and i, where students
are required to use logarithms.
 The
examples are based on first time home
buyers.
 Calculations of monthly payments are based
on the affordable home price for first time
home buyer.
 Example: Calculate the monthly payment for
a $90,000 home. Loan is for30 year fixed rate
at 5% annual interest with 20% down
payment.

The formula listed below is used:
M = Monthly payment
 R = Interest rate
 N = Number of years

Students are asked to try the calculations for
different loan amount at different interest rate.
 Students are also asked to calculate the amount
of interest paid to the lender.

 CJ
and Heather decided to establish a savings
account at the SPC credit union for Taylor,
their newborn baby girl, that would provide
her with $48,000 college expenses at the
age of 18 . The manager of the credit union
advised them that they can deposit a certain
amount at 10% compounded semiannually to
reach their goal. How much money would
they need to deposit in her savings account?
P
= unknown amount to be deposited
 A = $48,000, I = 10%/2 = 0.05 , n = 2 x 18 = 36
 Therefore, P = A(1 + i)^(-n)
= $48,000(1.05)^(-36)
= $48,000(.172657415)
= $8,287.56
 www.kiplinger.com
 www.money.com
 www.cnnfn.com
 www.cnbc.com
 www.daveramsey.com

Azimova, M. (2010). Student Debt and Financial Literacy,
Business Today online Journal, Retrieved on March 27, 2013

Quick Facts about Student Dept (2010),
http://projectonstudentdebt.org/files/File/Debt_Facts_and_Sou
rces.pdf. Retrieved on March 26, 2013

Walsh, K. (2011). 10 Reasons Why Schools Should Be Teaching
Financial Literacy To Our Kids,
http://www.emergingedtech.com/2011/04/10-reasons-whyschools-should-be-teaching-financial-literacy-to-our-kids.
Retrieved on March 28, 2013




Default Rates Continue to Rise for Federal Student Loans
(September 30, 2013)
http://www.ed.gov/news/press-releases/default-rates-continuerise-federal-student-loan. Retrieved on October 3, 2013