Math for Liberal Arts MAT 110: Chapter 4 Notes Taking Control of - - PowerPoint PPT Presentation

MAT 110, Chapter 4 1

Math for Liberal Arts MAT 110: Chapter 4 Notes

Managing Money David J. Gisch

Taking Control of Your Finances

Controlling Y

• ur Finances
• Know your bank balance.

▫ Never bounce a check or have a debit card rejected.

• Know what you spend.

▫ Keep track of debit and credit card spending.

• Don’t buy on impulse.

▫ Think first; buy only if the purchase makes sense.

• Make a budget, and don’t overspend

it.

▫ Many people do not do this. Number one mistake!!!!!

A Four-S tep budget

1. List all monthly income, including a prorated am ount for any incom e not received m onthly (such as once-a-year payments).

• 2. List all monthly expenses, including a prorated

am ount for expenses that don’t recur m onthly.

• 3. Subtract total expenses from total income to determine

your net monthly cash flow.

• 4. Make adjustments as needed.

MAT 110, Chapter 4 2

Net Cash Flow

Net cash flow is the amount you have left at the end of a period. Computing your net cash flow is vital when budgeting your money!

• If you have a positive net cash flow, then great. Maybe

consider saving or investing more.

• If your net cash flow is negative you need to cut expenses
• r try to increase your income, the latter of which is

usually hard. For most people, the most difficult part is making sure you do not leave anything out.

Prorating

• Prorating just means that you turn all amounts into a

certain unit of measure. For budgeting, that is often the amount per month. Example: Dave orders a Venti-Iced-No Whip-Peppermint- Mocha and a reduced fat* turkey-bacon sandwich at Starbucks about once a week. It is his Friday treat after a hard week of disseminating knowledge to America's future. About how much does he spend a year if the cost is $8.50 for the two items?

*The no-whip and reduced fat turkey bacon makes it ok, right?

College Expenses

Example: You pay $3500 for tuition, $750 in student fees, and $500 for textbooks each semester. How should you handle these expenses in computing your monthly budget? Assume you attend 2 semesters a year.

Net Cash Flow

Example : The following shows income and expenses for an

• individual. Find the monthly net cash flow. Assume income

is after taxes and that 52 1 4 1 .

MAT 110, Chapter 4 3

• 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

section 4D)

• Understand how taxes are computed and how

they can affect your financial decisions. (This is in section 4E, 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)

Base Financial Goals on S

• lid Understanding

The Power of Compounding

I have the power!

If compounding interest were a cartoon character.

Definitions & Formulas

• The principal in financial formulas is the balance upon

which interest is paid.

• Sim ple interest is interest paid only on the original

principal, and not on any interest added at later dates.

• Com pound interest is interest paid on both the
• riginal principal and on all interest that has been added

to the original principal.

Sim ple Interest 1 A = Amount after t years I = Interest Earned P = Principal or Initial Amount r = rate of interest (percent as a decimal) t = time in years

Definitions & Formulas

• Note that compound interest can accrue multiple times a

year ( value).

▫ Annually, 1 ▫ Semi-Annually, 2 ▫ Quarterly, 4 ▫ Monthly, 12 ▫ Daily, 365.

Compound Interest 1

• 1
• A = Amount after t years

P = Principal or Initial Amount r = rate of interest (percent as a decimal) n = number of times compounded per year. t = time in years

These compound interest formulas should be thought of as Lump-Sum (one-time payment) scenarios.

MAT 110, Chapter 4 4

S imple and Compound Interest

Example : Compare the growth in a $100 investment for 5 years at 10% simple interest per year and at 10% interest compounded annually.

S imple and Compound Interest

Sim ple Interest* Com pound Interest*

End

• f

Year Interest Paid Old Balance + New Balance 1 1000 .10 1 100 1000 100 1100 2 1000 .10 1 100 1100 100 1200 3 1000 .10 1 100 1200 100 1300 4 1000 .10 1 100 1300 100 1400 5 1000 .10 1 100 1400 100 1500 End

• f

Year Interest Paid Old Balance + New Balance 1 1000 .10 1 100 1000 100 1100 2 1100 .10 1 110 1100 110 1210 3 1210 .10 1 121 1210 121 1331 4 1331 .10 1 133.10 1331 133.10 1464.10 5 1464.10 .10 1 146.41 1464.10 146.41 1610.51

Example : Compare the growth in a $1000 investment for 5 years at 10% simple interest per year and at 10% interest compounded annually.

*Remember, simple interest is only on the original amount, being $100. *Since it is compounding, the interest is calculated using the newest balance.

You ended with $110.51 more! It would be even greater if it was compounded multiple times a year.

S imple and Compound Interest

Example : You invest $500 in an account with an APR of 5%. (a) Calculate the future amount after 8 years using simple interest. (b) Calculate the future amount after 8 years using quarterly compounding interest.

1 5001 .058 1

• 500 1 .05

4

∗

S imple and Compound Interest

Example : You invest $200 in an account with an APR of 8% when you are 20. (a) Calculate the future amount when you are 65 using simple interest. (b) Calculate the future amount when you are 65 using monthly compounding interest.

1 2001 .08 45 1

• 200 1 .08

12

∗

MAT 110, Chapter 4 5

Annual Percentage Yield

• 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  A loan with 6% interest compounded semi-annually

• Note: APY>APR

APY=5.12% APY=6.09%

US Bank Example

Savings Plans and Investments

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). ▫ 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.

MAT 110, Chapter 4 6

Mutual Fund

• Both types of IRA’s pool your money in with everyone

else who invest in the “general fund” and it is used to buy several stocks. Therefore it is less risky than buying individual stocks on your own.

S tocks

• Very risky as your money is all in on one company.
• You make money by selling your stock for more than you

purchased it or when the company pays out dividends to its stock holders.

▫ 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.

MAT 110, Chapter 4 7

Why Annuities?

• It is Guaranteed.
• Lots of options.

▫ Life ▫ Cash refund. ▫ Period certain ▫ Etc

Annuities (S avings Plan Formula)

Annuities (Savings Plan Formula)

A PMT 1 r n

• 1

r n PMT A r n 1 r n

• 1

A = Amount after t years. PMT = Payments Amount r = rate of interest (percent as a decimal) n = number of times compounded per year. t = time in years

• An annuity is any series of equal, regular payments.
• The future value, A, of an annuity is the accumulated

amount at some future date.

Annuities

Example : You decide to dedicate some money every month into an annuity. You find you can manage $100 a month on which you earn, on average, 8% interest compounded monthly. If you started when you were 20, how much would you have at age 60?

A PMT 1 r n

• 1

r n 100 1 .08 12

∗

1 .08 12 $349,100.78 *If you don’t type it in as one “chunk” carry out your decimal at least 6-8 places!!!! 2327.3386 .0067 $347,363.97 2327.338554 .006667 $349,083.33 2327.338554 .00666667 $349,100.61

Advantages of Annuities (from )

• Unlike other tax-deferred retirement accounts such as 401(k)s

and IRAs, there is no annual contribution limit for an annuity. That allows you to put away more money for retirement, and is particularly useful for those that are closest to retirement age and need to catch up.

• All the money you invest compounds year after year without

any tax bill from Uncle Sam. That ability to keep every dollar invested working for you can be a big advantage over taxable investments.

• When you cash out, you can choose to take a lump-sum

payment from your annuity, but many retirees prefer to set up guaranteed payments for a specific length of time or the rest

• f your life, providing a steady stream of income.
• The annuity serves as a complement to other retirement

income sources, such as Social Security and pension plans.

MAT 110, Chapter 4 8

S avings

Example : You have a child and want to save $100,000 for their college expenses. If you will invest for 17 years at an average rate of 6.5%, how much should your monthly payments be?

PMT A r n 1 r n

• 1

PMT 100,000 .065 12 1 .065 12

∗

1 $269.45

Total and Annual Return

The total return is the relative change in the investment.

• The annual return is the annual percentage yield (APY)

that would give the same overall growth.

• 1

S tocks/ Investments

Example : Suppose that you decided to invest in some real estate property in the year 2004. The amount of your

• riginal investment is $27,500. In the year 2013 you

decide to sell and receive $43,400 for the property. What is your total return?

S tocks/ Investments

Example : You buy 12 shares of Google stock at $540 a

• share. You sell it 3 years later at $574 a share. What is your

total and annual return?

MAT 110, Chapter 4 9

Financial Planning Tips

• Handout
• The contents of this handout are considered class

reading and the contents are therefore eligible for test questions.

Loan Payments, Credit Cards, and Mortgages

Credit S core

• Your credit score greatly effects your interest rate on
• loans. (↓ ↑

Loan Basics

• The principal is the amount of money owed at any

particular time.

• An installm ent loan (or amortized loan) is a loan that

is paid off with equal regular payments.

• An am ortization schedule is a table of principal and

interest payments over the life of a loan.

MAT 110, Chapter 4 10

Understanding Amortization

• You make the same

payment each month.

• The amount of interest

you pay that month is calculated using simple interest

▫ , here is

• because time is measured

in years for simple interest but it is the interest for 1 month. ▫ P is the current balance of the loan. ▫ After interest is taken out

• f your payment, whatever

is left goes toward your balance.

For example. Say you owe $5000 on a loan charging 5% interest and your monthly payment is $125 5000 .05 1 12

• $20.83

$125 $20.83 $104.17 $5000 $104.17 $4895.83

Amortization Table

Example : What is your balance after Month 4?

Note: They use 0.0075 as it is equal to .09 ⁄ 0.0075.

Calculating Loan Payments

• This formula works for any type of installment loan

where you pay off what you borrowed with equal payments over time.

• On www.gischsource.com I have a link to an online

amortization calculator.

• You can also get amortization calculators for free as a cell

phone app.

Am ortization (Loan Paym ent Form ula)

• 1 1
• Credit Cards

Credit cards differ from installment loans in that you are not required to pay off your balance in any set period of time.

• A minimum monthly payment is required.
• Monthly payment generally covers all the interest but

very little principal.

• It takes a very long time to pay off a credit card loan if
• nly the minimum payments are made.

MAT 110, Chapter 4 11

Credit Cards

Example : Suppose you have a balance of $3,200 on your credit card which has an APR of 23% (or 1.92% per month). (a) If the minimum monthly payment is ⁄

• f the

previous months balance, what is your minimum payment amount? (b) If you made no more charges, what would your payment be if you wanted to pay off your credit card in 2 years?

Loan Payments

Example: Suppose you have $15,000 in student loans upon graduation. The interest rate is 5.25% and the term

• f the loan is 20 years.

(a) What are your monthly payments? (b) How much will you pay over the lifetime of the loan? (c) How much did you pay in interest?

• 1 1
• 15,000 .0525

12 1 1 .0525 12

∗ $101.08

Mortgages

• The longer the loan, the more money in interest you pay.

▫ For example, $175,000 for the house PLUS $163,000 in interest

• n a 25 year loan!!!!

Mortgages

• A hom e m ortgage is an installment loan designed

specifically to finance a home.

▫ The mortgage is the amount AFTER your down payment.

• The down paym ent is the amount of money you must

pay up front in order to be given a mortgage or other loan.

• Closing costs are fees you must pay in order to be

given the loan. These include direct costs, or fees charged as points, where each point is 1% of the loan amount.

▫ For example, if your mortgage is $100,000 and the closing cost is 3 points, it is $100,000.03 $3,000

MAT 110, Chapter 4 12

Mortgages

Example: You want to buy a house and your mortgage would be $125,000 at a rate of 4.75% for 30 years. Your closing costs are $1200 plus 2 points. (a) What are your monthly payments? (b) How much did you pay at closing? (c) How much will you pay over the lifetime of the loan? (d) How much did you pay in interest and fees?

• 1 1
• 125,000 .0475

12 1 1 .0475 12

∗ $652.06

A Closer Look at Amortization

• The bank gets most of their money in interest at the

beginning of the loan.

• In this example the payment is $734 over 30 years at 8%

interest.

A Closer Look at Amortization

• The same $734 payment show in an amortization table.

Taxes

MAT 110, Chapter 4 13

Taxes

• You will not have homework nor be tested over taxes.
• We are taxed using what is called a progressive tax
• bracket. It is NOT a flat percentage.

Tax Bracket Married Filing Jointly Single 10% Bracket $0 – $17,400 $0 – $8,700 15% Bracket $17,400 – $70,700 $8,700 – $35,350 25% Bracket $70,700 – $142,700 $35,350 – $85,650 28% Bracket $142,700 – $217,450 $85,650 – $178,650 33% Bracket $217,450 – $388,350 $178,650 – $388,350 35% Bracket Over $388,350 Over $388,350 $75,000

Taxes

• Lets say you (and your spouse together) make $75,000.

People often would say, “Oh, I pay 25% in taxes.” This not TRUE!!!!!

▫ You get an exemption (approximately $5000 for each family member) subtracted from your income. So let’s say this is for a husband and wife with 1 child, that would give us $75,000 3 5,000 $60,000 ▫ Then you subtract any legal deductions determined by the IRS tax

• code. Deductions can include: Interest paid on home mortgage,

interest paid on student loans, contributions to 401(k), medical deferment account, work related expenses, etc. You subtract this

• r a minimum of $12,000 (for a couple), whichever is higher. So

now we have $60,000 12,000 $48,000 or less

Taxes

• So you actually only pay taxes on $48,000, or possibly less if you

had a lot of deductions. ▫ Looking back at the chart you then assume you pay 15% of $48,000, but you don’t. ▫ You pay 10% on $17,400. After you take out $17,400 you get $48,000 $17,400 $30,600 ▫ You then pay 15% on the remaining $30,600. ▫ So you pay the following in taxes. 17,400 .10 30,600 .15 $6,330

• This is effectively paying 8.44% of your income in taxes. That is a

huge difference in paying 25% as originally claimed. 6330 75000 0.0844 8.44%

Tax Bracket Married Filing Jointly Single 10% Bracket $0 – $17,400 $0 – $8,700 15% Bracket $17,400 – $70,700 $8,700 – $35,350

Taxes

• Or think of it this way.

$48,000 $17,400 $30,600 You pay 10% on this portion. $1,740 You pay 15% on this portion. $4,590 Together that is $6,330. Amount left of your $75,000 after exemptions and deductions. $6,330 is only 8.84% of $75,000.

Tax Bracket Married Filing Jointly Single 10% Bracket $0 – $17,400 $0 – $8,700 15% Bracket $17,400 – $70,700 $8,700 – $35,350

MAT 110, Chapter 4 14

Business and Investments

• Business get taxed too but it is a little different. However,

they have tons of deduction possibilities. This allowed Bank of America to pay $0.00 in taxes in 2010.

• Also, income made on investments such as stocks, some

retirement accounts, etc are taxed with a flat 15% tax rate known as the capital gains tax.

• Some states have taxes, like Iowa, but whatever you pay

in state tax can be deducted from your federal taxes.