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

2. Vocabulary
interest
simple interest
principal

3. When you keep money in a savings account, your money earns 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.

4. 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.
Simple interest is money paid only on the principal
Rate of interest is the percent charged or earned
I = P · r · t
Time that the money is borrowed or invested (in years)
Principal is the amount borrowed or invested
Notice that the interest rate is expressed as a decimal and the time is expressed in years.

5. Additional Example 1: Using the Simple Interest Formula
Find the missing value.
A. I =
, P = $575, r = 8%, t = 3 years
I = P · r · t
I = 575 · 0.08 · 3
Substitute. Use 0.08 for 8%.
I = $138
Multiply.
The simple interest is $

6. Additional Example 1: Using the Simple Interest Formula
Find the missing value.
B. I = $204, P = $1,700, r =
, t = 6 years
I = P · r · t
204 = 1,700 · r · 6
Substitute.
204 = 10,200r
Multiply.
204
10,200 =
10,200r
Divide each side by 10,200.
0.02 = r
The interest rate is 2%.

7. Check It Out! Example 1
Find the missing value.
A. I =
, P = $525, r = 7%, t = 2 years
I = P · r · t
I = 525 · 0.07 · 2
Substitute. Use 0.07 for 7%.
I = $73.50
Multiply.
The simple interest is $73.50.

8. Check It Out! Example 1
Find the missing value.
B. I = $600, P = $2,000, r =
, t = 3 years
I = P · r · t
600 = 2,000 · r · 3
Substitute.
600 = 6,000r
Multiply.
600
6000 =
6,000r
6,000
Divide each side by 6,000.
0.1 = r
The interest rate is 10%.

9. Understand the Problem
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? 1
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.

10. Additional Example 2 Continued
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.

11. Additional Example 2 Continued
Solve. 3
A = P + I
Substitute.
6,800 = 6,000 + I
–6,000 – 6,000
Subtract from each side.
800 = I
I = P · r · t
800 = 6,000 · 0.04 · t
Substitute. Use 0.04 for 4%.
800 = 240t
Multiply.
800
240 =
240t
Divide each side by 240.
3.33  t
Round to the nearest hundredth. 1 3
It will take 3
years.

12. Additional Example 2 Continued4
Look Back 1 3
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
= 800 1 3
An answer of 3 years for the account to reach
$6,800 makes sense.

13. Understand the Problem
Check 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? 1
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.

14. Check It Out! Example 2 Continued
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.

15. Check It Out! Example 2 Continued
Solve 3
A = P + I
Substitute.
12,000 = 10,000 + I
–10,000 –10,000
Subtract 10,000 from each side.
2,000 = I
I = P · r · t
2,000 = 10,000 · 0.08 · t
Substitute. Use 0.08 for 8%.
2,000 = 800t
Multiply.
2,000
800 =
800t
Divide each side by 800.
2.5 = t 1 2
It will take 2
years.

16. Check It Out! Example 2 Continued4
Look Back 1 2
After exactly 2 years, Linda’s money will have
earned $2,000 in simple interest and her account
balance will be $12,000. 1 2
I = 10,000 · 0.08 · 2
= 12,000 1 2
An answer of 2 years for the account to reach
$12,000 makes sense.