6-6 Simple Interest

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpMultiply.

1. 800 0.04 3

2. 1,700 2 0.25

3. 900 0.05 4

4. 1,200 6 0.35

96

850

180

Course 2

6-6 Simple Interest

2,520

Problem of the DayWhich number does not belong in the group?

0.75 75%

Course 2

6-6 Simple Interest

34

68

751,000

751,000

= ;340

the others equal . 34

Learn to solve problems involving simple interest.

Course 2

6-6 Simple Interest

Vocabulary

interestsimple interestprincipal

Insert Lesson Title Here

Course 2

6-6 Simple Interest

Course 2

6-6 Simple Interest

When you keep money in a savings account, your money earns interest. Interest is an amount that is collected or paid for the use of money. For example, the bank pays you interest to use your money to conduct its business. Likewise, when you borrow money from the bank, the bank collects interest on its loan to you.

Course 2

6-6 Simple Interest

One type of interest, called simple interest, is money paid only on the principal. The principal is the amount of money deposited or borrowed. To solve problems involving simple interest, you can use the following formula.

I = P · r · t

Interest

Principal

Rate of interest per year(as a decimal)

Time in years that themoney earns interest

Find the missing value.

Additional Example 1A: Using the Simple Interest Formula

Course 2

6-6 Simple Interest

A. I = , P = $575, r = 8%, t = 3 years

I = P · r · t

I = 575 · 0.08 · 3

I = $138

The simple interest is $138.00.

Substitute. Use 0.08 for 8%.

Multiply.

Find the missing value.

Additional Example 1B: Using the Simple Interest Formula

Course 2

6-6 Simple Interest

B. I = $204, P = $1,700, r = , t = 6 years

I = P · r · t

204 = 1,700 · r · 6

204 = 10,200r

20410,200

= 10,200r10,200

0.02 = r

The interest rate is 2%

Substitute.

Multiply.

Divide by 10,200 to isolate the variable.

Find the missing value.

Try This: Example 1A

Course 2

6-6 Simple Interest

A. I = , P = $525, r = 7%, t = 2 years

I = P · r · t

I = 525 · 0.07 · 2

I = $73.50

The simple interest is $73.50.

Substitute. Use 0.07 for 7%.

Multiply.

Find the missing value.

Try This: Example 1B

Course 2

6-6 Simple Interest

B. I = $600, P = $2,000, r = , t = 3 years

I = P · r · t

600 = 2,000 · r · 3

600 = 6,000r

6006000

= 6,000r6,000

0.1 = r

The interest rate is 10%

Substitute.

Multiply.

Divide by 10,200 to isolate the variable.

Additional Example 2: Problem Solving Application

Avery deposits $6,000 in an account that earns 4% simple interest. How long will it take for his account balance to reach $6,800?

Insert Lesson Title Here

Course 2

6-6 Simple Interest

11 Understand the Problem

Rewrite the question as a statement:• Find the number of years it will take for Avery’s account to reach $6,800.

List the important information:• The principal is $6,000.• The interest rate is 4%.• His account balance will be $6,800.

Insert Lesson Title Here

Course 2

6-6 Simple Interest

22 Make a Plan

Avery’s account balance A includes the principal plus the interest: A = P + I. Once you solve for I, you can use I = P · r · t to find the time.

Additional Example 2: Problem Solving Application

Avery deposits $6,000 in an account that earns 4% simple interest. How long will it take for his account balance to reach $6,800?

Course 2

6-6 Simple Interest

Solve33A = P + I

6,800 = 6,000 + I

800 = I

I = P · r · t800 = 6,000 · 0.04 · t800 = 240t

3.33 tIt will take 3 1

3years.

Substitute.

Subtract to isolate the variable.

Substitute. Use 0.04 for 4%.Multiply.

Divide to isolate the variable.

Round to the nearest hundredth.

Additional Example 2: Problem Solving Application

–6,000 – 6,000

800240

= 240t240

Course 2

6-6 Simple Interest

Look Back44

After exactly 3 years, Avery’s money will have earned $800 in simple interest and his account balance will be $6,800.

13

I = 6,000 · 0.04 · 3 13

= 800

So it will take 3 years to reach $6,800.13

Additional Example 2: Problem Solving Application

Try This: Example 2

Linda deposits $10,000 in an account that earns 8% simple interest. How long will it take for the total amount in her account to reach $12,000?

Insert Lesson Title Here

Course 2

6-6 Simple Interest

11 Understand the Problem

Rewrite the question as a statement:• Find the number of years it will take for Linda’s account to reach $12,000.

List the important information:• The principal is $10,000.• The interest rate is 8%.• Her account balance will be $12,000.

Insert Lesson Title Here

Course 2

6-6 Simple Interest

22 Make a Plan

Linda’s account balance A includes the principal plus the interest: A = P + I. Once you solve for I, you can use I = P · r · t to find the time.

Try This: Example 2

Linda deposits $10,000 in an account that earns 8% simple interest. How long will it take for the total amount in her account to reach $12,000?

Course 2

6-6 Simple Interest

Solve33A = P + I

12,000 = 10,000 + I

2,000 = I

I = P · r · t2,000 = 10,000 · 0.08 · t2,000 = 800t

2.5 = tIt will take 2 1

2years.

Substitute.

Subtract to isolate the variable.

Substitute. Use 0.08 for 8%.Multiply.

Divide to isolate the variable.

–10,000 –10,000

Try This: Example 2

2,000 800

= 800t800

Course 2

6-6 Simple Interest

Look Back44

After exactly 2 years, Linda’s money will have earned $2,000 in simple interest and her account balance will be $12,000.

12

I = 10,000 · 0.08 · 2 12

= 12,000

So it will take 2 years to reach $12,000.12

Try This: Example 2

Lesson Quiz

Find each missing value.

1. I =

2. I = $18, P = $150, r =

3. I = $640, P =

4. I = $120, P = $600, r = 5% t =

6%

$240

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$2,000

4 years

Course 2

6-6 Simple Interest

, P = $800, r = 10%, t = 3 years

, t = 2 years

, r = 4%, t = 8 years

5. Dennis deposits $6,000 in an account that earns 5.5% simple interest. How long will it take before the total amount is $8,000?

a little over 6 years