7. Financial Literacy
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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.
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Lesson Settings & Tools
| | 9 Theory slides |
| | 9 Exercises - Grade E - A |
| | Each lesson is meant to take 1-2 classroom sessions |
Financial Literacy
Slide of 9
This lesson focuses on the 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, a general understanding of these concepts and confidence in managing financial matters will be increased.
Catch-Up and Review
Here are a few recommended readings before getting started with this lesson.
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Challenge
Leaving a Tip
Vincenzo went out for dinner together with his family. The total cost of the meal was $124. Because they really enjoyed the food and the service, they left a 20 % tip.
External credits: studiogstock
How much tip did they leave?
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Discussion
Interest
Interest is the cost of borrowing money from a bank or 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
The 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 a product of principal, annual interest rate, and the time in years.
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 instance, assume that a savings account earns 3% simple interest per year on a deposit of $1000. 1000 * 0.03* 1= $ 30 This means that 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 |
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Example
Calculating the Amount of Interest
Vincenzo is a very thrifty child and saves some of his allowance every month. His father thinks that opening a savings account for Vincenzo's savings would be great for him. He wants to support Vincenzo and plans to deposit $5000 in this account as principal.
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?
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b If an account earns $100 in 4 years, what is the annual interest rate that the bank offers?
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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 Notice that the balance is the final amount of money in the account after adding the interest. The amount of principal is $5000 and the bank offers 4 % simple interest for this amount. Using this information, the interest for Vincenzo's savings account can be calculated. Recall the simple interest formula to find the amount of interest.
I= P r t In this formula, I is the amount of interest, P is the principal, r is the annual interest rate, and t is the time in years. Since Vincenzo's money will stay in this account for 10 years, substitute the values P= 5000, r= 4 %, and t= 10 into the formula to calculate the total amount of interest.
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. As a final step, add this amount to the principal to calculate the final balance in 10 years. 5000+ 2000=7000 The balance of the account will be $7000 after 10 years.
b This time the amount of interest earned in 4 years is given. Since the values of principal, time, and the amount of interest are known, the formula for simple interest can be applied again.
I= P r t Substitute these values into the formula and solve for the annual interest rate 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.
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Example
Who is Correct?
Vincenzo goes to Miami, Florida, to visit his aunt and uncle. The city's sales tax rate is 7 %. Vincenzo wants to buy a new coat. The price of the coat before tax is $120. Vincenzo says that the total cost can be calculated by finding 7 % of $120 and adding this value to $120.
However, the salesperson says that to find the selling price, the price of the coat $120 needs to be multiplied by 1.07. Who is correct?
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Hint
Calculate the total cost using the methods described by Vincenzo and the salesperson. Use the percent equation to calculate the amount of the tax.
Solution
It is given that the sales tax rate in Miami is 7 %. This means that to purchase an item, an additional 7 % of its original price must be paid as sales and use tax.
Selling Price=Original Price + Tax
Calculate the tax for a $120 coat in two ways to determine who is correct, Vincenzo or the salesperson.
Vincenzo's Way
Vincenzo prefers to calculate the total cost in two steps, by finding 7 % of $120 and then adding this amount to the original price of the coat. Recall that a percent of a number can be calculated as a product of the percent and that number. The percent equation can be helpful to do that. a= p % * w In this equation, a represents the amount of tax, p is the percent, and w is the original price of the item. Substitute the values into the percent equation and calculate 7 % of $120. Remember to write the percent as a decimal number.
a=p % * w
SubstituteII
p= 7, w= 120
a= 7 % * 120
PercentToFrac
a %=a/100
a=7/100 * 120
MoveRightFacToNum
a/c* b = a* b/c
a=840/100
CalcQuot
Calculate quotient
a=8.40
The amount of the tax for a $120 coat is $8.40. Now add this amount to the original price of the coat to find the total cost. 120+ 8.40=128.40 Vincenzo can buy this coat for $128.40. Next, calculate the total cost following the salseperson's method.
The salesperson's Way
The salesperson calculates the total cost by multiplying $120 by 1.07. Check the result to see if it is the same as Vincenzo's solution.
120 * 1.07
WriteSum
Write as a sum
120 * (1+0.07)
Distr
Distribute 120
120* 1 + 120 * 0.07
Multiply
Multiply
120+8.40
AddTerms
Add terms
128.40
According to the salesperson's calculations, the total cost of the coat is $128.40.
Conclusion
Notice that both methods gave the same result. This is because multiplying 120 by 7 %, or 7100, and adding the result to 120 is the same as multiplying 120 by 1.07. 120 * 7/100 + 120 ⇔ 120 * (1.07) Both of the ways are correct and give the same total cost. This means that both Vincenzo and the salesperson are correct.
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Example
Calculating the Markup and Markdown
Vincenzo visits several more shopping centers in Miami. He buys a pair of sneakers and some jeans at a department store. Below is his receipt.
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b A few days later, Vincenzo saw the same shoes on an online shopping platform. He noticed that the price in-store had a 20 % markup compared to the price online. What is the price of the sneakers online? Round the answer to two decimal places.
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Hint
a Discount or markdown refer to a reduction in the price of an item.
b Markup refers here to the difference between the price in-store and the price online.
Solution
a Vincenzo received a $10 discount on the jeans, but the percent of that discount is unknown. Start by examining the receipt to find this amount as a percent.
According to the receipt, the jeans cost $34.00 and Vincenzo received a discount of $10.00. Now, recall the formula for the percent equation. a=p % * w In the percent equation, the part of the whole a is the percent p multiplied by the whole w. Here, the discount of 10.00 dollars is the part a, the percent is p, and the whole w is the original price, 34.00 dollars.
a=p % * w
SubstituteII
a= 10.00, w= 34.00
10.00= p %* 34.00
▼
Solve for p
RearrangeEqn
Rearrange equation
p % * 34.00 =10.00
DivEqn
.LHS /34.00.=.RHS /34.00.
p % =10.00/34.00
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 Vincenzo noticed that the price of the sneakers in store includes a 20 % markup compared to the price online. To find the price online, start by adding 20 % to 100 %.
100 % + 20 %= 120 % The in-store price of the sneakers is 120 % of the price online. Now, recall the formula for the percent equation once again. a= p % * w According to the receipt, the in-store price of the sneakers is $ 44.00. This represents the part a. The percent is 120 and the whole w is the price online. Now, solve the equation for w.
a=p % * w
SubstituteII
a= 44.00, p % = 120 %
44.00= 120 %* w
▼
Solve for w
PercentToFrac
a %=a/100
44.00=120/100* w
MoveRightFacToNum
a/c* b = a* b/c
44.00=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.
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Example
Calculating a Bonus
Vincenzo's aunt signed an agreement when she joined a company two years ago. If she is still working with the company after two years, she will receive a bonus equivalent to 8 % of the contract's total value.
If Vincenzo's aunt makes $1200 a month, how much money will she make as a bonus?
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Hint
Calculate the total amount of money that she earns in twenty-four months, then calculate 8 % of that amount.
Solution
Start by calculating the total value of the contract. Since Vincenzo's aunt earns $1200 per month, multiply this amount by 24 to find the total amount of money that she earns in two years.
1200 * 24 = 28 800
She earns 28 800 dollars in two years. Per her contract, 8 % of this amount will be given as a bonus. The percent equation can be used to calculate 8 % of 28 800.
a= p % * w
Recall that the part a is equal to the product of the percent p and the whole w. Substitute p %= 8 % and w= 28 800 into the percent equation to find the value of a.
a=p % * w
SubstituteII
p= 8, w= 28 800
a= 8 % * 28 800
PercentToFrac
a %=a/100
a=8/100* 28 800
MoveRightFacToNum
a/c* b = a* b/c
a=8* 28 800/100
SplitIntoFactors
Split into factors
a=8* 288 * 100/100
CancelCommonFac
Cancel out common factors
a=8* 288 * 100/100
SimpQuot
Simplify quotient
a=8* 288
Multiply
Multiply
a=2304
Vincenzo's aunt will get $2304 as a bonus after working for the company for two years.
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Example
Paying Back a Loan
Vincenzo's uncle 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.
a Help Vincenzo's uncle calculate how much money he will pay in interest.
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b How much will he pay back altogether?
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Hint
a Start by using the percent equation to find the amount of interest Vincenzo's uncle will pay over one year.
b Add the amount of the loan to the total amount of interest found in Part A.
Solution
a Remember that simple interest represents a proportional relationship between the annual interest and the principal, or initial amount, of a certain amount of money. The ratio of annual interest to the principal is the interest rate.
Vincenzo's uncle wants to know how much money he will pay in interest. Start by using the percent equation to find the amount of interest he will pay in one year. part = percent * whole ↓ interest amount = interest rate * principal In this case, the principal of the loan is $ 2400 and the interest rate is 3.5 %. Let the interest amount be represented by s. For simplicity, ignore the units for now. interest amount = interest rate * principal ↓ s = 3.5 % * 2400 Next, solve the equation for s. Remember that percents can be written as decimals by moving the decimal point two places to the left.
This means that the simple interest for one year is equal to $ 84. Finally, multiply the interest for one year by 4 to calculate the total amount of interest that Vincenzo's uncle will pay over 4 years. $ 84 * 4 = $ 336 Vincenzo's uncle will pay $ 336 in total in interest. It is worth keeping in mind that this amount can be found directly by using the simple interest formula. In this formula, I is the amount of interest, P is the principal, r is the interest rate, and t is the time in years. P r t=I ⇓ 2400 * 3.5% * 4 = 336
b To find out how much Vincenzo's uncle will pay in total when repaying the loan, add the principal to the total amount of interest. Remember that it was found in Part A that Vincenzo's uncle will pay $336 in total in interest over the four years of the loan.
$ 2400 + $ 336= $ 2736 This means that he will pay $ 2736 altogether when repaying the loan.
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Closure
Calculating the Amount of Tip
The challenge presented at the beginning of the lesson was to find 20 % of $124 in order to find the amount to tip. As done in the previous examples, use the percent equation to calculate a percent of the whole. a= p% * w Note that the percent p is 20 % and the total cost of the meal represents the whole, which is $124. Now substitute these values into the percent equation. a= 20 %* $124 Evaluate the right-hand side of the equation to find the value of a. Remember to rewrite the percent as a fraction.
a=20% * 124
PercentToFrac
a %=a/100
a=20/100 * 124
MoveRightFacToNum
a/c* b = a* b/c
a=20 * 124/100
Multiply
Multiply
a=2480/100
CalcQuot
Calculate quotient
a=24.80
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Financial Literacy
Exercise 1.1
Match the given concepts with the correct definitions.
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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 |
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Solution
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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.
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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.
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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.
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Solution
Select the words that represent an increase in the final amount to be paid.
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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.
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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?
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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 %.
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Financial Literacy
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