SIMPLE

AND

COMPOUND INTEREST

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

SLIDE 2Chapter 18

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.

SLIDE 3Chapter 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.

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.

SLIDE 4Chapter 18

SLIDE 5Chapter 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.

SLIDE 6Chapter 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.

SLIDE 7Chapter 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.

SLIDE 8Chapter 18

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).

(continued)

SLIDE 9Chapter 18

Avoiding UnnecessaryCredit 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.

SLIDE 10Chapter 18

Avoiding UnnecessaryCredit 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.

(continued)

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

Chapter 18

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

• The cost is based on three elements: 1. A loan’s principal is the amount borrowed,

or the unpaid portion of the amount borrowed, on which the borrower pays interest.

2. The rate is the percentage of interest you will pay on a loan.

3. Time is the period during which the borrower will repay a loan; it is expressed as a fraction of a year.

(continued)

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

Annual interest rate

IMPLE INTEREST FORMULA

Interest paid

Principal(Amount of money invested or borrowed)

Time (in years)I = PRT

1,000

.07

5

350.00

Simple Interest Equation: Step 1

P(Principal)

r(Interest Rate

)

t(Time Period)

I(Interest Earned)

$1,000 invested at 7% interest rate for 5 years

Simple Interest Equation: Step 2

P(Principal)

I (Intere

st Earne

d)

A(Amoun

t Investm

ent is Worth)

$1,000 invested at 7% interest rate for 5 years

1,000 350

$1,350.0

0

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.

10 = (200)(0.04)T

1.25 yrs = TTypically 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).

enter in formula as a decimal I = PRT

100

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:

Step Two:

600.00 .012 1 7.20

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

amount at the end

Principal(amount at start)

annual interest rate

(as a decimal)nt

n

rPA

1

time(in

years)

number of times per year that interest in

compounded

Compound Interest Equation – Single Sum

P (1 + r)n = A

$1,000 invested at 7% interest rate compounded yearly for 5 years

1,000 (1+ .07)5 = $1403.00

Principal (1 + Interest Rate)Time Periods =Amount

Investment is Worth

nt

n

rPA

1500

.08

4

4 (2)

83.585$A

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%

Find the amount that results from $500 invested at 8% compounded quarterly after a period of 2 years.

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:

%375.14/5.5

Compound Interest

• So for our IRA account of $5000 at the end of a year looks like:

• After 10 years, we have:

72.5280$4

055.015000

14

1

F

85.8633$4

055.015000

104

10

F

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.

tn

n

rPF

1

Compound InterestPeriod Interest

CreditedTimesCreditedper year

Rate percompounding period

Annual year 1 R

Semiannual 6 months 2

Quarterly quarter 4

Monthly month 12

2R

4R

12R

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 yearsCompounding Method Amount Investment is

Worth

Daily $1,419.02Monthly $1,417.63Quartely $1,414.78

Semi-Annually $1,410.60Annually $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:

336$607.800$ PRTI

58.400$800$58.1200$

58.1200$)07.1(800$)1( 6

PMI

iPM n

Example 2• Example: $32000 is invested at 10% for 2

years. Find the interest compounded yearly, semiannually, quarterly, and monthly yearly:

semiannually:

20.6896$32000$20.38896$

20.38896$)05.1(32000$)1( 4

PMI

iPM n

6720$32000$38720$

38720$)10.1(32000$)1( 2

PMI

iPM n

Example 2 (cont.)• Example: (continued)

quarterly:

monthly:

20.7052$32000$20.39052$

20.39052$)00833.1(32000$)1(

24212%,833.24

12%10

PMI

iPM

nin

89.6988$32000$89.38988$

89.38988$)025.1(32000$)1( 8

PMI

iPM n

Now it’s time to……….

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