Contemporary Mathematics

# Key Concepts

## 6.1Understanding Percent

• Know what a percent is as a fraction, a decimal, and as a part of the whole.
• Use the percent equation to find any of the three values that are related by the equation.
• Apply the percent equation in applications.

## 6.2Discounts, Markups, and Sales Tax

• Discounts are markdowns from an original price.
• Mark-ups are increases to the price paid by a retailer to cover their costs.
• be able to calculate the markup based on a percentage of the cost
• Sales taxes vary from state to state and often county to county.
• Retail prices, sales prices and percent discounts can be calculated if the other two values are known.
• Original costs, retail prices, and percent markup can be calculated if the other two values are known.
• In calculations, sales tax acts like a markup.

## 6.3Simple Interest

• Interest is money that is paid by a borrower for the privilege of borrowing the money.
• Simple interest is computed by substituting the principal, interest rate, and number of years into the formula $I=P×r×tI=P×r×t$
• The payoff for a loan is the amount of principal remaining on a loan plus the interest that accumulated on the loan since the last payment.
• The future value of an investment yielding simple interest is the original principal plus the interest earned on the investment.
• When making a partial payment, some of the payment pays off all the accumulated interest, while the remainder of the payment is applied to the principal of the loan.
• Finding the present value of an investment is used to determine how much should be invested now in order to achieve a specific goal.

## 6.4Compound Interest

• Compound interest means that the interest earned during one period will earn interest in later periods. Essentially, the amount of the principal grows from period to period.
• The important values in computing compound interest are the interest rate, the principal, the length of time the investment, and the number of times the investment is compounded.
• Compound interest has minimal impact early, but later has a very large impact.
• You can determine how much to invest today in order to reach a goal for some time later.
• Compound interest can be translated into an effective annual yield, which allows for comparison between investment options.

## 6.5Making a Personal Budget

• A budget is a set of guidelines for how to allocate your income.
• Budgeting helps to plan for many of life’s expenses
• Budgets are used to compare income to expenses. When expenses exceed income, changes have to be made.
• Budgets can help evaluate the affordability of life changes.
• One guideline for setting a budget is the 50-30-20 budget philosophy. The guidelines suggest that 50% of income is allocated to necessary expenses, 30% to expenses that wants, and 20% to savings and other debt reduction.

## 6.6Methods of Savings

• There are three main types of savings accounts, saving accounts, certificates of deposit (CD), and money market accounts.
• Savings account are very risk free, and so yield low interest rates.
• The differences in the three types of savings accounts relate to their convenience.
• Savings account typically have a lower interest rate that money market accounts, which typically have lower interest rates than CDs.
• Ordinary annuities more accurately reflect how we save, in that money is deposited repeatedly over time.
• Spreadsheet software, such as Google Sheets, have built in functions that can be used to quickly calculate both the future value of an ordinary annuity account, but also the payment necessary to reach a goal using an ordinary annuity.

## 6.7Investments

• There are many different investments with different returns and risks.
• Bonds are loans form the purchaser to the entity selling the bond.
• Bonds have some tax benefits, low to no risk, and a low return.
• Stocks represent part ownership in a company. As such, stock holders share in the profits, and losses, of the company.
• Information, including price, P/E, yearly highs and lows, and dividend amount can be found in online stock tables available on many websites.
• Mutual funds represent collections of professionally administered investment vehicles. Have shares in a mutual fund has lower risk than ownership of stocks.
• Retirement accounts employ some of the same strategies as mutual funds, in that they spread the risk and are professionally managed.
• IRAs and Roth IRAs differ on when taxes are paid on the money, and who can use them. Roth IRAs have income limits while traditional IRAs do not.

## 6.8The Basics of Loans

• There are many reasons for a loan, but primarily it is taken out for a large expense when cash is not available.
• Each payment for an installment loan consists of an interest portion and a principal portion.
• There is a formula to calculate the payment necessary to pay off a loan in installments.
• Amortization schedules, or tables, show how each payment is applied to principal and interest. It also includes other details such as remaining balance and total interest paid.
• Loans often have other fees associated with them such as origination fees or application fees. The total of the interest paid and the fees is the cost of finance.

## 6.9Understanding Student Loans

• The FAFSA must be filled out each year that a student wishes to borrow for.
• A student’s funding gap determines how much they need in loans to pay for college.
• Federal subsidized student loans defer payments until after graduation and interest does not accrue on these loans.
• Unsubsidized student loans defer payment until after graduation but interest begins accruing as soon as the loan finds are disbursed.
• There are both yearly and aggregate limits for student loans to prevent over-borrowing, among other reasons.
• Federal direct loans have a low interest rate set by the government, but other student loans have varying rates of interest set by the banks.
• The standard repayment plan lasts 10 years and is made up of monthly payments.
• Consolidating or refinancing student loans merges many student loans into one loan.
• If only federal loans are consolidated, the interest rate is the same as the individual loans, currently set at 4.99%.
• If other loans are refinanced together, the interest rate may be lower with the new loan.
• Other repayment plans are available. Such a plan may have payment that start small and grow as the loan is paid off, or it may have a longer term, or may be based on the discretionary income of the student.
• Being delinquent on a student loan is a precursor to being in default. Making payments in a timely fashion allows the student to avoid this situation.

## 6.10Credit Cards

• Credit cards can be a flexible way to pay for almost anything, but can become a financial hazard if used unwisely.
• When deciding which credit card to apply for, evaluate the interest rate, fees (annual and late), reward programs and credit limit. Be sure they meet your criteria.
• Paying off the balance of your credit card every month will control your spending and will never result in paying interest.
• Credit card statements hold all important information about your credit card, including payment, balances, charges and billing cycle dates.
• Although the minimum payment is attractive precisely because it is so small, paying only the minimum results is a long payoff term and higher interest costs.

## 6.11Buying or Leasing a Car

• There are many factors to consider when choosing to buy or lease a car.
• The cost of the car is increased by a number of fees and sales tax.
• There are advantages to buying a car and advantages to leasing a car. The decision between the two depends on the preference of the buyer.
• Insurance covers costs associate with accidents. It is made up of various components.
• The costs of owning a car, including insurance and maintenance, should be a part of the budgeting process.
• Budgeting for unexpected repairs can ease the stress of encountering large repair bill.

## 6.12Renting and Homeownership

• There are many points of comparison between renting and buying a house.
• Before deciding to buy a house, you should carefully consider all the responsibilities that come with home ownership.
• Renting comes with more restrictions on the renter, but with fewer costs and is easier to move from.
• Owning a house has more costs but has more freedom, plus the owner creates equity.
• Mortgages are loans, and payments are calculated in the same way as any other loan.
• Amortization tables help a homeowner understand the mortgage and how the payments are applied to the principal and interest.
• In addition to paying the amount financed for a mortgage, the monthly payment will include an escrow payment, which covers insurance and taxes.

## 6.13Income Tax

• Federal income tax is based on income after certain adjustments.
• Gross income is income from all sources, including gifts and winnings.
• Before taxes are calculated, the taxable income is found by subtracting deductions and exemptions from gross income.
• Income tax is progressive, increasing in rate as income increases.
• Being in the 32% tax bracket means some of your income is taxed at 10%, some at 12%, some at 22%, some at 24%, and the rest at 32%.
• Income in each tax bracket is taxed at that bracket’s rate, which means in 2022 the first \$10,275 earned is taxed at 10% only.
• Tax credits are subtracted from the taxes that are owed.
• Some tax credits are refundable, which means they can make the amount you owe negative, which results in a refund.