SIMPLE AND COMPOUND INTEREST Since this section involves what can happen to your money, it should be of INTEREST to you!

Goals for today: I can…. Discuss how to protect your credit accounts from fraud. Compute and explain simple interest and APR. Compute and explain compound interest. Chapter 18

Protecting Yourself from Credit Card Fraud Credit card fraud costs businesses and consumers millions of dollars each year. Common types of fraud Illegal use of a lost or stolen credit card Illegal use of credit card information intercepted online While the credit card holder’s liability is limited to $50, the merchant is not protected from loss. Merchants often raise their overall prices to cover such losses. Chapter 18

How to Prevent Credit Card Fraud Always keep a list of credit and charge cards and their numbers in a safe place—not in your wallet. Notify issues immediately when a loss occurs, both on the phone and with a follow-up letter. Keep a copy of all sales receipts so you can verify the accuracy of the monthly statement. Chapter 18

Safeguarding Your Cards Sign and activate cards immediately. Carry only cards you need. Keep a list of cards and information about them in a safe place. Notify creditors if a card is lost or stolen. Watch card during transactions. Tear up old receipts. Chapter 18

Safeguarding Your Cards Do not lend cards or leave them lying around. Destroy expired cards. Do not give credit card information by phone or online to people or businesses you don’t know. Keep receipts and verify charges on statements. Chapter 18

Protecting Your Accounts Online Deal with companies you know and trust. Look for secure site symbol. Encryption is a code that protects your account name, number, and other information. When information is encrypted, it is made unreadable to others trying to read it. Review privacy policy. Chapter 18

Protecting Your Accounts Online (continued) Protecting Your Accounts Online Look for the seal of a non-profit watchdog group. Initiate all transactions yourself at sites you trust. Phishing is a scam that uses online pop-up messages or e-mail to deceive you into disclosing personal information. “Phishers” send messages that appear to be from a business that you normally deal with, such as your bank or Internet service provider (ISP). Chapter 18

Avoiding Unnecessary Credit Costs Accept only the amount of credit that you need. Unused credit can count against you. Unused credit is the remaining credit available to you on current accounts. Make more than the minimum payment. Do not increase spending as income increases. Keep your credit accounts to a minimum. Pay cash for small purchases. Chapter 18

Avoiding Unnecessary Credit Costs (continued) Avoiding Unnecessary Credit Costs Understand the cost of credit. Shop for loans. Take advantage of credit incentive programs. With a rewards program, you will receive a payback in the form of points that can be redeemed for merchandise or airline tickets. With a rebate plan, you get back a portion of what you spent in credit purchases over the year. Chapter 18

2 types of Interest Simple interest – interest is paid only on the principal Compound interest – interest is paid on both principal and interest, compounded at regular intervals

Example a $1000 principal paying 10% simple interest after 3 years pays .1  3  $1000 = $300 If interest is compounded annually, it pays .1  $1000 = $100 the first year, . 1  $1100 = $110 the second year and .1  $1210 = $121 the third year totaling $100 + $110 + $121 = $331 interest

Computing the Cost of Credit The cost of credit is determined by using the formula for simple interest. Simple interest is computed on the amount borrowed only and without compounding. Chapter 18

Simple Interest Formula (continued) Simple Interest Formula The cost is based on three elements: A loan’s principal is the amount borrowed, or the unpaid portion of the amount borrowed, on which the borrower pays interest. The rate is the percentage of interest you will pay on a loan. Time is the period during which the borrower will repay a loan; it is expressed as a fraction of a year. Chapter 18

Simple Interest The length of time the borrower will take to repay a loan is expressed as a fraction of a year—twelve months, fifty-two weeks, or 360 days. Six months = ½ Three months = ¼ 90 days = 90/360 or 1/4 Chapter 18

I = PRT IMPLE INTEREST FORMULA Annual interest rate Interest paid Time (in years) Principal (Amount of money invested or borrowed)

Simple Interest Equation: Step 1 (Principal) P (Interest Rate) r (Time Period) t (Interest Earned) I 1,000 .07 5 350.00 $1,000 invested at 7% interest rate for 5 years

Simple Interest Equation: Step 2 (Principal) P (Interest Earned) I (Amount Investment is Worth) A $1,000 invested at 7% interest rate for 5 years 1,000 350 $1,350.00

If you invested $200.00 in an account that paid simple interest, find how long you’d need to leave it in at 4% interest to make $10.00. enter in formula as a decimal I = PRT 100 10 = (200)(0.04)T 1.25 yrs = T Typically interest is NOT simple interest but is paid semi-annually (twice a year), quarterly (4 times per year), monthly (12 times per year), or even daily (365 times per year).

Time Value of Money Math Practice #1 Sara deposited $600.00 into a savings account one year ago. She has been earning 1.2% in annual simple interest. Complete the following calculations to determine how much Sara’s money is now worth. Step One: 600.00 .012 1 7.20 Step Two: 600.00 7.20 607.20

Time Value of Money Math Practice #1 How much is Sara’s investment worth after one year? $607.20

Compound Interest Notice that the interest in our account was paid at regular intervals, in this case every year, while our money remained in the account. This is called compounding annually OR one time per year.

Compound Interest Here’s a quick YouTube video that might help to simplify things

COMPOUND INTEREST FORMULA annual interest rate (as a decimal) Principal (amount at start) time (in years) amount at the end number of times per year that interest in compounded

Compound Interest Equation – Single Sum P (1 + r)n = A Amount Investment is Worth Principal (1 + Interest Rate)Time Periods = $1,000 invested at 7% interest rate compounded yearly for 5 years 1,000 (1+ .07)5 = $1403.00

Find the amount that results from $500 invested at 8% compounded quarterly after a period of 2 years. 4 (2) .08 500 4 Effective rate of interest is the equivalent annual simple rate of interest that would yield the same amount as that made compounding. This is found by finding the interest made when compounded and subbing that in the simple interest formula and solving for rate. Find the effective rate of interest for the problem above. The interest made was $85.83. Use the simple interest formula and solve for r to get the effective rate of interest. I = Prt 85.83=(500)r(2) r = .08583 = 8.583%

Compound Interest Suppose that instead of collecting interest at the end of each year, we decided to collect interest at the end of each quarter, so our interest is paid four times each year. What would happen to our investment? Since our account has an interest rate of 5.5% annually, we need to adjust this rate so that we get interest on a quarterly basis. The quarterly rate is:

Compound Interest So for our IRA account of $5000 at the end of a year looks like: After 10 years, we have:

Compound Interest Formula P dollars invested at an annual rate r, compounded n times per year, has a value of F dollars after t years. Think of P as the present value, and F as the future value of the deposit.

Compound Interest Period Interest Credited Times Credited per year Rate per compounding period Annual year 1 R Semiannual 6 months 2 Quarterly quarter 4 Monthly month 12

$1,000 invested at 7% for 5 years Amount Investment is Worth Compound Interest Number of times interest is compounded has effect on return Interest compounding frequently will yield higher returns $1,000 invested at 7% for 5 years Compounding Method Amount Investment is Worth Daily $1,419.02 Monthly $1,417.63 Quartely $1,414.78 Semi-Annually $1,410.60 Annually $1,402.55

Example 1 Example: $800 is invested at 7% for 6 years. Find the simple interest and the interest compounded annually Simple interest: Compound interest:

Example 2 Example: $32000 is invested at 10% for 2 years. Find the interest compounded yearly, semiannually, quarterly, and monthly yearly: semiannually:

Example 2 (cont.) Example: (continued) quarterly: monthly:

Now it’s time to………. Go to kahoot.it