6-7 Simple Interest

IWBAT solve problems involving simple

interest.

6-7 Simple Interest

Vocabulary

interest

simple interest

principal

6-7 Simple Interest

WRITE: When you keep money in a savings account, your money earns interest. Interest is an amount that is charged for borrowing or using money, or an amount of money that is earned by saving 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.

6-7 Simple Interest

WRITE:

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 the money earns interest

6-7 Simple Interest

Find the missing value.

EX 1A: Using the Simple Interest Formula

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.

6-7 Simple Interest

Find the missing value.

EX 1B: Using the Simple Interest Formula

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

I = P · r · t

204 = 1,700 · r · 6

204 = 10,200r

204 10,200

= 10,200r 10,200

0.02 = r

The interest rate is 2%

Substitute.

Multiply.

Divide by 10,200 to isolate the variable.

6-7 Simple Interest

EX 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?

1 Study the Problem and Organize the Facts

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.

6-7 Simple Interest

2 Line up 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.

EX 2 Continued

6-7 Simple Interest

Verify the Plan with Action 3

A = P + I

6,800 = 6,000 + I

800 = I

I = P · r · t 800 = 6,000 · 0.04 · t

800 = 240t

3.33 t

It will take 3 1 3

years.

Substitute.

Subtract to isolate the variable.

Substitute. Use 0.04 for 4%.

Multiply.

Divide to isolate the variable.

Round to the nearest hundredth.

–6,000 – 6,000

800 240

= 240t 240

EX 2 Continued

6-7 Simple Interest

Evaluate Your Solution 4

After exactly 3 years, Avery’s money will have

earned $800 in simple interest and his account balance will be $6,800.

1 3

I = 6,000 · 0.04 · 3 1 3

= 800

So it will take 3 years to reach $6,800.

1 3

EX 2 Continued