Holt CA Course 1

6-7 Simple Interest

NS1.4 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips.Also covered: AF1.1

California Standards

Holt CA Course 1

6-7 Simple Interest

Vocabulary

interestsimple interestprincipal

Holt CA Course 1

6-7 Simple InterestWhen 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.

Holt CA Course 1

6-7 Simple InterestOne 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

Simple interest is money paid only on the principal

Principal is the amount borrowed or invested

Rate of interest is the percent charged or earned

Time that the money is borrowed or invested (in years)

Notice that the interest rate is expressed as a decimal and the time is expressed in years.

Holt CA Course 1

6-7 Simple Interest

Find the missing value.

Additional Example 1: Using the Simple Interest Formula

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.

Holt CA Course 1

6-7 Simple Interest

Find the missing value.

Additional Example 1: Using the Simple Interest Formula

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 each side by 10,200.

Holt CA Course 1

6-7 Simple Interest

Find the missing value.

Check It Out! Example 1

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.

Holt CA Course 1

6-7 Simple Interest

Find the missing value.

Check It Out! Example 1

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 each side by 6,000.

Holt CA Course 1

6-7 Simple InterestAdditional 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?

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.

Holt CA Course 1

6-7 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 Continued

Holt CA Course 1

6-7 Simple Interest

Solve.33

A = P + I

6,800 = 6,000 + I

800 = I

I = P · r · t800 = 6,000 · 0.04 · t

800 = 240t

3.33 tIt will take 3

13 years.

Substitute.

Subtract from each side.

Substitute. Use 0.04 for 4%.

Multiply.

Divide each side by 240.

Round to the nearest hundredth.

–6,000 – 6,000

800240

= 240t240

Additional Example 2 Continued

Holt CA Course 1

6-7 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

An answer of 3 years for the account to reach

$6,800 makes sense.

13

Additional Example 2 Continued

Holt CA Course 1

6-7 Simple InterestCheck It Out! 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?

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.

Holt CA Course 1

6-7 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.

Check It Out! Example 2 Continued

Holt CA Course 1

6-7 Simple Interest

Solve33A = P + I

12,000 = 10,000 + I

2,000 = II = P · r · t

2,000 = 10,000 · 0.08 · t2,000 = 800t

2.5 = tIt will take 2

12 years.

Substitute.

Subtract 10,000 from each side.

Substitute. Use 0.08 for 8%.

Multiply.

Divide each side by 800.

–10,000 –10,000

2,000 800

= 800t800

Check It Out! Example 2 Continued

Holt CA Course 1

6-7 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

An answer of 2 years for the account to reach

$12,000 makes sense.

12

Check It Out! Example 2 Continued