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Pre-Algebra View details
7. Financial Literacy
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Pre-Algebra /
Chapter 5
7. 

Financial Literacy

This lesson offers an in-depth look at financial literacy, specifically honing in on the concepts of simple interest and sales tax. Simple interest is the extra money you either earn from savings or owe when you borrow. Understanding this can help you make smarter decisions about loans or investments. Sales tax, on the other hand, is the additional cost you pay when purchasing goods. Being savvy about sales tax can help you budget more effectively. For example, knowing the sales tax rate can help you anticipate the final price of a product, avoiding surprises at the checkout. These concepts are not just theoretical; they have real-world applications that can affect your financial health.

Student Learning Objectives:
  • Understand and calculate simple interest
  • Calculate percent increase and decrease in the form of markup and discount
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9 Theory slides
9 Exercises - Grade E - A
Each lesson is meant to take 1-2 classroom sessions
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Financial Literacy
Slide of 9
This lesson focuses on several ways to manage money and explores some related concepts. Concepts such as sales tax, markup, discount, markdown, principal, and simple interest will be introduced through examples. By the end of the lesson, students will gain a general understanding of these concepts and confidence in managing financial matters.

Catch-Up and Review
Here are a few recommended readings before getting started with this lesson.

Challenge

Leaving a Tip

Vincenzo went out for dinner with his family. The total cost of the meal was $124. They left a 20 % tip.

tipbox image
External credits: studiogstock

How much tip did they leave?

Discussion

Interest

Interest is the cost of borrowing money from a bank or the additional money earned from keeping money in a bank account. There are several types of interest, but only simple interest will be introduced in this lesson.

Concept

Simple Interest

Interest that is applied only to an initial amount of money is called simple interest. The initial amount is known as the principal. Simple interest is calculated as the product of the principal, the annual interest rate, and the time in years.

Simple Interest Formula: I=Prt, where I is simple interest, P is principal, r is the annual interest rate, and t is time.

An interest rate is a percent used to calculate the interest on the principal. It may be easier to write it in decimal form to make the calculations easier. For example, assume that a savings account earns 3 % simple interest per year on a deposit of $1000. 1000 * 0.03* 1= $ 30 The simple interest earned on $1000 in one year is $30. The final amount of money in the account is called the balance. The following table shows the balance over five years of an account that earns 3 % simple interest each year.

Years  Amount of Simple Interest  Balance
1 1000 * 0.03* 1=$ 30 1000+30=$ 1030
2 1000 * 0.03* 2=$ 60 1000+60=$ 1060
3 1000 * 0.03* 3=$ 90 1000+90=$ 1090
4 1000 * 0.03* 4=$ 120 1000+120=$ 1120
5 1000 * 0.03* 5=$ 150 1000+150=$ 1150
Notice that the balance at the end of each period is calculated by adding the principal and simple interest earned during that period.
Example

Calculating the Amount of Interest

Vincenzo's father wants to open a college savings account for him with $5000 in the account as principal. Savings.jpg After talking with several bankers, he notices that banks offer different interest rates.

a

If the bank offers 4 % simple interest per year, what will be the balance after 10 years?

b

If an account earns $100 in 4 years, what is the annual interest rate that the bank offers?

Hint
a

Use the simple interest formula.

b

Substitute the given values into the simple interest formula and solve the equation for r.

Solution
a

The balance is the final amount of money in the account after adding the interest to the principal. The principal is $5000, and the bank offers 4 % simple interest. We can use the simple interest formula to find the interest in Vincenzo's college account after 10 years.

I=Prt
SubstituteValues

Substitute values

I= 5000 * 4 % * 10
WriteDec

Write as a decimal

I=5000 * 0.04 * 10
Multiply

Multiply

I=2000

The account will earn $2000 in 10 years. Finally, we add the interest to the principal to find the balance after 10 years. 5000+2000=7000 The balance of the account will be $7000 after 10 years.

b

This time, we know that an account with a principal of $5000 earns $100 in 4 years, and we want to find the annual interest rate. We can substitute these values into the simple interest formula and solve for r.

I=Prt
SubstituteValues

Substitute values

100= 5000 * r * 4
▼
Solve for r
Multiply

Multiply

100=20 000r
DivEqn

.LHS /20 000.=.RHS /20 000.

100/20 000=r
ReduceFrac

a/b=.a /100./.b /100.

1/200=r
WriteDec

Write as a decimal

0.005 =r
WritePercent

Convert to percent

0.5 %=r
RearrangeEqn

Rearrange equation

r=0.5 %

The bank offers a 0.5 % annual interest rate.

Example

Who is Correct?

Thomas wants to buy a new coat. The price of the coat before tax is $120. The city's sales tax rate is 7 %. Thomas says that the total cost can be calculated by finding 7 % of $120 and adding this value to $120. Taxes.jpg However, the salesperson says that to find the total cost, the price of the coat $120 needs to be multiplied by 1.07. Who is correct?

Hint
Calculate the total cost using both methods.

Solution
To purchase an item, an additional 7 % of its original price must be paid as tax. To determine who is correct, we review how Thomas and the salesperson calculate the total cost on a $120 coat.

Thomas's Way

Thomas calculates the total cost in two steps. First, he finds 7 % of $120 — the tax. Then, he adds the tax to the original price of the coat. To find the tax, we multiply 7 % by $120.

7 % * 120
▼
Simplify
PercentToFrac

a %=a/100

7/100 * 120
MoveRightFacToNum

a/c* b = a* b/c

840/100
CalcQuot

Calculate quotient

8.40

Now we can find the total cost by adding the original price and the tax. $ 120+ $ 8.40= $ 128.40 Thomas calculates the total cost of the coat as $128.40.

The Salesperson's Way

The salesperson calculates the total cost by multiplying $120 by 1.07. If we write 1.07 as a percent, we get 107 %. This means the salesperson calculates 107 % of the original price of the coat, including the tax, in one step.

1.07 * 120
▼
Simplify
WriteAsFrac

Write as a fraction

107/100 * 120
MoveLeftFacToNum

a*b/c= a* b/c

107 * 120/100
Multiply

Multiply

12 840/100
CalcQuot

Calculate quotient

128.40

Using the salesperson's method, the total cost of the coat is also $128.40.

Conclusion

Both Thomas and the salesperson calculated the price of the pants correctly. The difference is that Thomas calculates the tax first and adds it to the original price, while the salesperson combines both steps into one multiplication. price + 7 % * price = 107 % * price
Example

Calculating the Markup and Markdown

Ramsha purchases some new school clothes. Below is her receipt.

Receipt showing the prices as jeans:$34, sneakers:$44,discount:-$10, sales tax:$1.95, total:$69.95
a

Ramsha received a $10 discount on the jeans she purchased. What percent discount did she receive on them? Round the answer to the nearest whole percent.

b

A few days later, Ramsha saw the same shoes on an online shopping platform. She noticed that the in-store price had a 20 % markup compared to the price online. What is the price of the sneakers online?

Hint
a

Discount or markdown refers to a reduction in the price of an item.

b

Markup refers here to the difference between the in-store price and the price online.

Solution
a

Ramsha received a $10 discount on jeans that originally cost $34. Let's use the percent equation to find the percent discount.

a=p % * w Here, the discount $ 10 is the part a, the percent is p, and the original price $ 34 is the whole w.

a=p % * w
SubstituteII

a= 10, w= 34

10= p %* 34
▼
Solve for p
RearrangeEqn

Rearrange equation

p % * 34 =10
DivEqn

.LHS /34.=.RHS /34.

p % =10/34
UseCalc

Use a calculator

p % =0.294117 ...
WritePercent

Convert to percent

p % =29.4117 ... %
RoundInt

Round to nearest integer

p %≈ 29 %

The discount is equal to about 29 % of the original price.

b

Ramsha noticed that the price of the sneakers in the store includes a 20 % markup compared to the online price. This means that the in-store price is 120 % of the online price. We can substitute p= 120 and a= $ 44 into the percent equation and solve for w, the whole or online price.

a=p % * w
SubstituteII

a= 44, p % = 120 %

44= 120 %* w
▼
Solve for w
PercentToFrac

a %=a/100

44=120/100* w
MoveRightFacToNum

a/c* b = a* b/c

44=120w/100
MultEqn

LHS * 100=RHS* 100

4400=120w
DivEqn

.LHS /120.=.RHS /120.

4400/120=w
CalcQuot

Calculate quotient

36.666666 ... =w
RoundDec

Round to 2 decimal place(s)

36.67 ≈ w
RearrangeEqn

Rearrange equation

w ≈ 36.67

The price of the sneakers is about $36.67 on the online platform.

Example

Calculating a Bonus

Jessica signed an agreement when she started a part time job. If she is still working with the company at the end of her three month summer vacation, she will receive a bonus equivalent to 8 % of the contract's total value. Agreement.jpg If Jessica makes $1200 a month, how much money will she make as a bonus?

Hint
Calculate the total amount of money that she earns in 3 months, then calculate 8 % of that amount.

Solution
We start by calculating the total value of the contract. Since Jessica earns $1200 per month, we multiply this amount by 3 to find how much she earns in 3 months. 1200 * 3 = 3600 She will get 8 % of $3600 as a bonus if she is still working at the end of the summer. To find the bonus, we multiply 8 % by 3600.

8 % * 3600
PercentToFrac

a %=a/100

8/100* 3600
▼
Simplify right-hand side
MoveRightFacToNum

a/c* b = a* b/c

8* 3600/100
SplitIntoFactors

Split into factors

8* 36 * 100/100
CancelCommonFac

Cancel out common factors

8* 36 * 100/100
SimpQuot

Simplify quotient

8* 36
Multiply

Multiply

288

Jessica will get $288 as a bonus after working for the company for three months.

Example

Paying Back a Loan

Eric borrows $2400 to repair his car. He will pay off the loan over 4 years by paying back the principal plus 3.5 % simple interest for each year. Loan.jpg

a

Help Eric calculate how much money he will pay in interest.

b

How much will he pay back altogether?

Hint
a

Use the simple interest formula.

b

Add the amount of the loan to the total amount of interest found in Part A.

Solution
a

To find the amount of interest Eric will need to pay, we can use the simple interest formula.

I = P r t Here, the principal P is $2400, the annual interest rate r is 3.5 %, and the time t is 4 years. Let's substitute these values into the formula above and simplify.

I = P r t
SubstituteValues

Substitute values

I = 2400 * 3.5 % * 4
WriteDec

Write as a decimal

I = 2400 * 0.035 * 4
Multiply

Multiply

I = 336

Eric will pay $ 336 in total in interest.

b

To find how much Eric will pay in total to repay the loan, we add the principal to the total interest.

$ 2400 + $ 336= $ 2736 This means that he will pay $ 2736 altogether when repaying the loan.
Closure

Calculating the Tip Amount

The challenge at the beginning of the lesson was to find 20 % of $124 to calculate the tip. To do this, we multiply the percent by the amount of money and write the percent as a fraction.

20 % * 124
PercentToFrac

a %=a/100

20/100 * 124
MoveRightFacToNum

a/c* b = a* b/c

20 * 124/100
Multiply

Multiply

2480/100
CalcQuot

Calculate quotient

24.80

They left a $24.80 tip.



Level 1
Level 2
Level 3
Financial Literacy
Exercise 1.1

Match the given concepts with the correct definitions.

Let's recall the definitions of given concepts so we can pair up the options. Let's start with the sales tax.

Sales tax is an amount charged by the government that the customer pays in addition to the selling price for some product or service.

This means that sales tax is an additional amount of money charged on items or services. Next, let's consider when we might give a tip. In restaurants, we often give extra money to the server voluntarily when we are satisfied with the service. This is called a tip.

A tip is an amount of money above the cost of an item or service that is given in appreciation of the service.

Generally speaking, a store sells items for more than it pays for those items. This is how the store makes a profit. This amount of increase is called the markup. In other words, the markup is difference between the selling price and the cost of the item to the store.

Markup is the amount of increase from what the store pays for an item to the selling price of that item to the customer.

Finally, the selling price of an item or service is the amount that the customer pays for that item or service. It is the final price of the item or service after adding any markups or subtracting any discounts.

The selling price is the amount of that the customer pays for an item or service.

Let's finally pair the concepts and their definitions in a table.

Concept Definition
Sales Tax An additional amount that is added to the price of an item by the government
Tip Money a customer gives a worker above the price in return for a service
Markup The amount of increase from what the store pays to what the customer pays
Selling Price The amount that the customer pays for an item
E
Hint & Answer
S
Solution
Find the total cost of the given items. $ 980 laptop; 4 % tax

$ 32 dinner; 15 % tip

We want to find the selling price of the laptop. Let's start by calculating the dollar amount of the tax. We can then add it to the retail price. Let's use the percent equation to find the amount of tax to be paid. part = percent * whole We are given that the price of the laptop is $ 980 and the tax is 4 %. Let p represent the dollar amount of the tax. Our equation then takes the following form. p = 4 % * $ 980 We can write the percent as a decimal before we solve the equation. We do this by ignoring the percent symbol and moving the decimal point two places to the left. 4 % ⇔ 0.04 Now we can do the multiplication. Let's ignore the units for now for simplicity.

We got that p= 39.20. This means that the amount of tax is $ 39.20. Now we can calculate the total cost of the laptop by adding this amount to $ 980. $980 + $ 39.20 = $ 1019.20 This means that the total cost of the laptop is $ 1019.20.

We can use the percent equation again to find the amount of the tip. After that, we will add the tip amount to the price of the dinner to find the final cost. part = percent * whole We know that the dinner is $32, which corresponds to the value of the whole, and that the tip, or the percent, is 15 % of the whole. Let's calculate the value of part by substituting these values into the equation. Remember to rewrite the percent as a decimal number.

Since a tip is an additional amount of money given in return for a service, we will add this amount to the price of the dinner. This will give the total amount of money paid for the dinner. $32 + $ 4.80 = $ 36.80 The total cost of the dinner is $36.80.

E
Hint & Answer
S
Solution

A cell phone is on sale for 30 % off. If the sale price is $820, what is the original price of this phone? Round the answer to two decimal places.

We will use the percent equation to find the original price of the cell phone. part = percent * whole We are given that a cell phone costs $ 820 when it is on sale for 30 % off. This means that the sale price is 100 % -30 %, or 70 %, of the original price. If we let p represent the original price, then we have the following equation. $ 820 = 70 % * p Let's write the percent as a decimal before we solve the equation. We can do this by ignoring the percent symbol and moving the decimal point two places to the left.

This means that 70 % is equal to 0.70 or 0.7. $ 820 = 70 % * p [0.3em] ⇓ [0.3em] $ 820 = 0.7 * p Finally, we will solve the equation for p. We can ignore the units for now for simplicity.

We found that the original price of the cell phone is about $ 1171.43.

E
Hint & Answer
S
Solution

Select the words that represent an increase in the final amount to be paid.

We want to determine which of the given words increase the final amount of money to be paid. Let's recall the definitions of these terms.

Definition Explanation
Discount A decrease in the usual price of something Selling Price= Regular Price - Discount
Markup The amount of increase from what the store pays for an item to the price that the customer pays Price=Cost to Store + Markup
Tip Money a customer gives a worker in appreciation in return for a service Final Cost=Selling Price + Tip
Tax An amount charged by the government that the customer pays in addition to the price for some product or service Selling Price=Regular Price + Tax
Markdown The amount by which the regular price of item is decreased Selling Price=Regular Price - Markdown
Gratuity Money paid to a specific service worker to appreciate a job well-done Final Price=Regular Price + Gratuity

According to the table, we can say that markup, tip, gratuity, and tax represent an increase in the final amount of money to be paid, while discount and markdown reduce the price of an item or service.

E
Hint & Answer
S
Solution

Zosia's father received a $5200 loan from the bank. He plans on paying off the loan in 5 years. At the end of 5 years, he will have paid $1300 in interest. What is the simple interest rate on the bank loan?

If we borrow money from a bank, we pay the bank interest for the use of their money. We will use the simple interest formula to calculate the interest rate r that the bank charges on the loan given to Zosia's father. cl I= p r t, where & I =Interest & p& = Principal r& = Annual interest rate t& = Time (in years) We know that Zosia's father received a $5200 loan from the bank. He will pay $1300 interest over 5 years. I=1300 , p= 5200, t= 5 We want to calculate the annual interest rate r. Let's substitute these values into the simple interest formula and solve it for r.

The annual interest rate is 5 %.

E
Hint & Answer
S
Solution

Financial Literacy

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