Transcript Simple Interest Lesson 8.2.4 Lesson 1.1.1 8.2.4 Simple Interest California Standards: What it means for you: Number Sense 1.3 You’ll see what interest is and how to work out how.

Simple Interest
Lesson 8.2.4
Lesson
1.1.1
8.2.4
Simple Interest
California Standards:
What it means for you:
Number Sense 1.3
You’ll see what interest is and
how to work out how much
simple interest you could earn
over time.
Convert fractions to decimals and
percents and use these representations
in estimations, computations, and
applications.
Number Sense 1.6
Calculate the percentage of increases
and decreases of a quantity.
Number Sense 1.7
Solve problems that involve discounts,
markups, commissions, and profit and
compute simple and compound interest.
Key words:
•
•
•
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interest
simple interest
principle
interest rate
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Lesson
1.1.1
8.2.4
Simple Interest
Interest is an important real-life topic because
it’s all about saving and borrowing money.
If you keep your money in a savings account, the bank
will pay you something just for keeping it there.
The interest that you gain will be based on how
much you put in — and that means it’s another
use of percent increase.
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Lesson
1.1.1
8.2.4
Simple Interest
Interest is a Fee Paid For the Use of Money
When you keep money in a savings account, the bank
pays you interest for the privilege of using your money.
When you borrow money from a bank, the bank charges
you interest for the privilege of using their money.
Interest is a fee that you pay for using someone else’s money.
The interest to be paid is worked out as a percent of the
money invested or loaned.
The percent that is paid over a given time is called
the interest rate.
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Lesson
1.1.1
8.2.4
Simple Interest
Simple Interest is Paid Only on the Principal
The amount of money you put into or borrow from
a bank is called the principal.
Interest that is paid only on the principal is called
simple interest.
With simple interest, the interest rate tells you how
much money you will get back every year as a
percent of the principal.
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Lesson
1.1.1
8.2.4
Simple Interest
For example: think about depositing $100 in a savings
account with a simple interest rate of 5% per year.
For each year you leave your money in the account,
you will get 5% of $100 back.
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Lesson
8.2.4
Example
Simple Interest
1
You deposit $50 in a savings account that pays a simple
interest rate of 2% per year. How much interest will you get
over 3 years? How much will be in the account after 3 years?
Solution
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First find 2% of $50: $50 ×
= $1.
100
This is the amount of interest you will get each year.
So over 3 years you will earn: 3 × $1 = $3
After 3 years you will have:
$50 + (3 × $1) = $53 in the account.
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Solution follows…
Lesson
1.1.1
8.2.4
Simple Interest
Guided Practice
1. If you put money into a savings account which pays simple
interest, will the amount of interest you get in the first year be
the same as in the second year? Explain your answer.
Yes. Simple interest is calculated as a percent of the principle,
so you receive the same amount of interest each year.
2. You borrow $150 from a bank at a simple interest rate of
8% per year. How much interest will you pay in one year?
150 × (8 ÷ 100) = $12
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Solution follows…
Lesson
1.1.1
8.2.4
Simple Interest
Guided Practice
3. You deposit $200 in a savings account that pays a simple
interest rate of 5% per year. How much interest
will you get over 4 years?
200 × (5 ÷ 100) = 10
10 × 4 = $40
4. You deposit $65 in a savings account that pays a simple
interest rate of 4% per year. How much will be in your
account after 4 years?
65 × (4 ÷ 100) = 2.6
2.6 × 4 = 10.4
65 + 10.4 = $75.40
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Solution follows…
Lesson
1.1.1
8.2.4
Simple Interest
Use the Simple Interest Formula to Calculate Interest
In Example 1, to work out how much interest you got over
3 years, you worked out the percent of the principal that
you would get each year and multiplied it by 3.
So the calculation you did was:
This is the principle.
This is the time that the
money is in the account for.
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(50 ×
) × 3 = $3
100
This is the interest rate
written as a fraction.
This is the interest earned.
Now think about what each part of that equation represents.
You can use this to figure out a general formula for
finding simple interest.
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Lesson
1.1.1
8.2.4
Simple Interest
First assign a variable to stand for each part of the equation:
• P stands for the principal.
• r stands for the interest rate (in % per year),
written as a fraction or a decimal.
• t stands for time (in years).
• I stands for the amount of interest that has built up.
To find the amount of interest (I) that you got, you
multiplied together the principal (P), the interest rate (r),
and the time (t) the money was in the account for.
Written as a formula this is:
I = Prt
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Lesson
8.2.4
Example
Simple Interest
2
You deposit $276 in a savings account that has
a simple interest rate of 6% per year.
How much interest will you get over 5 years?
Solution
I = Prt
Write out the formula
I = $276 × 0.06 × 5
Substitute the values
I = $82.80
Do the multiplications
Over 5 years you’ll earn $82.80 interest.
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Solution follows…
Lesson
1.1.1
8.2.4
Simple Interest
Guided Practice
5. You borrow $57 from a bank at a simple interest rate of
9% per year. How much interest will you pay in one year?
I = Prt = 57 × 0.09 × 1 = $5.13
6. You deposit $354 in a savings account that pays
a simple interest rate of 2.5% a year.
How much interest will you get over 7 years?
I = Prt = 354 × 0.025 × 7 = $61.95
7. You deposit $190 in a savings account that pays
a simple interest rate of 4% a year.
How much will be in your account after 4 years?
I = Prt = 190 × 0.04 × 4 = 30.40, and 190 + 30.40 = $220.40
8. You put $520 in a savings account with a simple
interest rate of 6% a year. You take it out after 6 months.
How much interest will you get?
I = Prt = 520 × 0.06 × 0.5 = $15.60
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Solution follows…
Lesson
8.2.4
Simple Interest
Independent Practice
1. You borrow $75 from a bank at a simple rate of 9% per
year. How much interest will you pay over 7 years? $47.25
2. You deposit $64 in a savings account that pays a simple
interest rate of 2.5% a year. How much will be in your
account after 17 years? $91.20
3. Ian put $4000 into a short-term investment for 3 months.
The simple interest rate was 5.2% per year. How much
interest did Ian earn? $52
4. Luz borrows money from a bank at a simple interest rate
of 5% a year. After 4 years she has paid $50 interest. How
much did she borrow?
$250
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Solution follows…
Lesson
8.2.4
Simple Interest
Independent Practice
5. Ty puts $50 in a savings account with a simple interest
rate of 3% a year. He works out what interest he will get
in 5 years. His calculation is shown on the right. What
error has he made? How much interest will he get?
Ty has used 3 instead of 0.03 to represent 3% in his calculation.
The correct calculation is: $50 × 0.03 × 5 = $7.50
6. Anna puts $50 in a savings account that
pays a simple interest rate of 5% a year.
After 4 years she takes out all the money,
and puts it in a new account that pays a
simple interest rate of 6% a year. She
leaves it there for 5 years. How much will
Anna have in total at the end of this time?
$78
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Solution follows…
Lesson
8.2.4
Simple Interest
Round Up
Interest is money that is paid as a fee for
using someone else’s money.
Simple interest means that each year you get back
a fixed percent of the initial amount you invested.
Make sure you understand how simple interest works.
You’ll use a lot of the same math in the next lesson
on compound interest.
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