6-7 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
6-7 Simple Interest
2,520
Problem of the DayWhich number does not belong in the group?
0.75 75%
Course 2
6-7 Simple Interest
34
68
751,000
751,000
= ;340
the others equal . 34
Course 2
6-7 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
6-7 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
6-7 Simple Interest
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
6-7 Simple Interest
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.
Check It Out: Example 1A
Course 2
6-7 Simple Interest
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.
Check It Out: Example 1B
Course 2
6-7 Simple Interest
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 6,000 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
6-7 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
6-7 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
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
6-7 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
13 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
800240
= 240t240
Additional Example 2 Continued
Course 2
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
So it will take 3 years to reach $6,800.13
Additional Example 2 Continued
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?
Insert Lesson Title Here
Course 2
6-7 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
6-7 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
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
6-7 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
12 years.
Substitute.
Subtract to isolate the variable.
Substitute. Use 0.08 for 8%.Multiply.
Divide to isolate the variable.
–10,000 –10,000
2,000 800
= 800t800
Check It Out: Example 2 Continued
Course 2
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
So it will take 2 years to reach $12,000.12
Check It Out: Example 2 Continued
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
Insert Lesson Title Here
$2,000
4 years
Course 2
6-7 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
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