MAT 110, Chapter 4 Math for Liberal Arts MAT 110: Chapter 4 Notes Taking Control of Your Finances Managing Money David J. Gisch Controlling Y our Finances A Four-S tep budget 1. List all monthly income, including a prorated • Know your bank balance. am ount for any incom e not received m onthly ▫ Never bounce a check or have a debit card rejected. (such as once-a-year payments). • Know what you spend. 2. List all monthly expenses, including a prorated ▫ Keep track of debit and credit card spending. am ount for expenses that don’t recur m onthly . • Don’t buy on impulse. ▫ Think first; buy only if the purchase makes sense. 3. Subtract total expenses from total income to determine your net monthly cash flow. • Make a budget, and don’t overspend 4. Make adjustments as needed. it. ▫ Many people do not do this. Number one mistake!!!!! 1
MAT 110, Chapter 4 Net Cash Flow Prorating Net cash flow is the amount you have left at the end of a • Prorating just means that you turn all amounts into a period. certain unit of measure. For budgeting, that is often the ��� ���� ���� � ������ ������ � ������� �������� amount per month. Computing your net cash flow is vital when budgeting your Example: Dave orders a Venti-Iced-No Whip-Peppermint- money! Mocha and a reduced fat* turkey-bacon sandwich at • If you have a positive net cash flow, then great. Maybe Starbucks about once a week. It is his Friday treat after a consider saving or investing more. hard week of disseminating knowledge to America's future. • If your net cash flow is negative you need to cut expenses About how much does he spend a year if the cost is $8.50 or try to increase your income, the latter of which is for the two items? usually hard. For most people, the most difficult part is making sure you do not leave anything out. *The no-whip and reduced fat turkey bacon makes it ok, right? College Expenses Net Cash Flow Example: You pay $3500 for tuition, $750 in student fees, Example : The following shows income and expenses for an and $500 for textbooks each semester. How should you individual. Find the monthly net cash flow. Assume income handle these expenses in computing your monthly budget? is after taxes and that 52 ����� � 1 ���� Assume you attend 2 semesters a year. �4 ����� � 1 ������ . 2
MAT 110, Chapter 4 Base Financial Goals on S olid Understanding • Find a way to make your budget allow for savings; understand how savings work and how to choose appropriate savings plans. (We learn about savings in Section 4C) • Understand the basic mathematics of loans. (We do this in I have the power! section 4D) • Understand how taxes are computed and how they can affect your financial decisions. (This is in section 4E, The Power of Compounding which we are skipping) • Understand how the federal budget affects future personal finances. (I listen to NPR a lot to stay informed on all U.S. and world issues) If compounding interest were a cartoon character. Definitions & Formulas Definitions & Formulas • The principal in financial formulas is the balance upon Compound Interest A = Amount after t years which interest is paid. � � � 1 � � ���� P = Principal or Initial Amount � r = rate of interest (percent as a decimal) • Sim ple interest is interest paid only on the original n = number of times compounded per principal, and not on any interest added at later dates. � � � 1 � � ����� year. � t = time in years • Com pound interest is interest paid on both the original principal and on all interest that has been added • Note that compound interest can accrue multiple times a to the original principal. year ( � value). ▫ Annually, � � 1 ▫ Semi-Annually, � � 2 Sim ple Interest These compound interest A = Amount after t years ▫ Quarterly, � � 4 formulas should be � � ��� I = Interest Earned ▫ Monthly, � � 12 thought of as Lump-Sum � � ��1 � ��� P = Principal or Initial Amount ▫ Daily, � � 365 . (one-time payment) r = rate of interest (percent as a scenarios. decimal) t = time in years 3
MAT 110, Chapter 4 S imple and Compound Interest S imple and Compound Interest Example : Compare the growth in a $1000 investment for Example : Compare the growth in a $100 investment for 5 5 years at 10% simple interest per year and at 10% interest years at 10% simple interest per year and at 10% interest compounded annually. compounded annually. Sim ple Interest* Com pound Interest* End Interest Paid Old Balance + New End Interest Paid Old Balance + New � � ��� � � ��� of Balance of Balance Year Year 1 1000 .10 1 � 100 1000 � 100 � 1100 1 1000 .10 1 � 100 1000 � 100 � 1100 2 1000 .10 1 � 100 1100 � 100 � 1200 2 1100 .10 1 � 110 1100 � 110 � 1210 3 1000 .10 1 � 100 1200 � 100 � 1300 3 1210 .10 1 � 121 1210 � 121 � 1331 4 1000 .10 1 � 100 1300 � 100 � 1400 4 1331 .10 1 � 133.10 1331 � 133.10 � 14 64.10 1000 .10 1 � 100 1400 � 100 � 1500 5 5 1464.10 .10 1 1464.10 � 146.41 � � 146.41 1 610.51 *Remember, simple interest is only on the original *Since it is compounding, the interest is calculated using the newest balance. amount, being $100. You ended with $110.51 more! It would be even greater if it was compounded multiple times a year. S imple and Compound Interest S imple and Compound Interest Example : You invest $500 in an account with an APR of Example : You invest $200 in an account with an APR of 5%. 8% when you are 20. (a) Calculate the future amount after 8 years using simple (a) Calculate the future amount when you are 65 using interest. simple interest. � � ��1 � ��� � � 500�1 � .05�8�� � � ��1 � ��� � � 200�1 � .08 45 � (b) Calculate the future amount after 8 years using (b) Calculate the future amount when you are 65 using quarterly compounding interest. monthly compounding interest. ��∗�� ���∗��� � � � 1 � � � � 500 1 � .05 � � � 1 � � � � 200 1 � .08 ���� ���� � 4 � 12 4
MAT 110, Chapter 4 Annual Percentage Yield US Bank Example • APY is not the actual rate. It is the simple interest rate you would need to achieve the same amount due to compounding interest over a year. ▫ WHAT???? ▫ Remember earlier, we had the $1000 over 5 years comparison. Compound Interest: $110 for a year. So to achieve $110 with simple interest we would have needed a rate of 11%. • Basically, APY allows you to compare loans with different terms. ▫ Which is better? A loan with 5% interest compounded monthly, or APY=5.12% A loan with 6% interest compounded semi-annually APY=6.09% • Note: APY>APR Common S avings Plans • Bank Savings Plans, CD’s, Bonds ▫ Guaranteed but extremely low interest rate. • IRA, 401(k) ▫ Take money out of your check which lowers your taxable income for that current year. ▫ It is taxed when you withdraw it. ▫ Companies often have matching plans (e.g. match up to 3% of your salary). Savings Plans and Investments ▫ Limits on amount you can contribute in a year. • ROTH IRA ▫ After your current income is taxed you then invest it. ▫ It is not taxed when you withdraw it at retirement. ▫ Limits on amount you can contribute in a year. 5
MAT 110, Chapter 4 Mutual Fund S tocks • Very risky as your money is all in on one company. • Both types of IRA’s pool your money in with everyone • You make money by selling your stock for more than you else who invest in the “general fund” and it is used to buy purchased it or when the company pays out dividends to several stocks. Therefore it is less risky than buying its stock holders. individual stocks on your own. ▫ When a corporation earns a profit or surplus, that money can be put to two uses: it can either be re-invested in the business (called retained earnings), or it can be distributed to shareholders (called a dividend) • A capital gains tax (CGT) is a tax on capital gains, profit from selling stocks, bonds, or from dividends. What’s a Dividend What is an Annuity • You purchase this “investment” from a company and the company pays out a stream of payments to the you at a later point in time. ▫ Annuities are primarily used as a means of securing a steady (think guaranteed) cash flow for an individual during their retirement years. • SPDIA ▫ Single Premium Deferred Income Annuity. ▫ Say you buy an annuity for $100,000 now and when you retire in 10 years you start getting $400 a month until you die. • SPIA ▫ Single Premium Income Annuity ▫ Say you buy an annuity for $100,000 at retirement and immediately you start getting $300 a month until you die. 6
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