Algebra And Personal FiNANCE 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 non-profit university was $27,650 – 29% higher than 2004. • In 2008, the average debt at a private for-profit 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.
. Facts and Figures from National Post Secondary Student AID study (NPSAS) • 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.
Kelly Walsh’s 10 reasons to teach financial literacy to the students. • 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
CLASS AND STUDENT INFORMATION • 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.
What is tHE ROLE of ALEGBRA in FINANCIAL MATHEMATICS • 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.
Specific TOPICS COVERED • 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.
Difference between SIMPLE and Compound Interest • 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.
Retirement planning • 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.
Personal Savings Example • 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.
Mortgage CALCUlations • 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.
PRESENT VALUE : • 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?
SOLUTION : • 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
Resources for financial Planning • www.kiplinger.com • www.money.com • www.cnnfn.com • www.cnbc.com • www.daveramsey.com
References • 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_Sources.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-why-schools-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-continue-rise-federal-student-loan.Retrieved on October 3, 2013