7. Financial Literacy
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Chapter 5
7.
Financial Literacy
| Student Learning Objectives: |
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Why
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.
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.
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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 2.1
Zosia earns 2.2 % per year in simple interest on a $2400 deposit over 5 years. Which scenario results in a higher increase in simple interest?
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Before we changing any numbers, let's use the simple interest formula to determine how much money Zosia earns on her deposit in the current situation. cl I= p r t, where & I =Interest & p& = Principal r& = Annual interest rate t& = Time (in years) We know that the principal is $ 2400, the annual interest rate is 2.2 %, and the time is 5 years. Let's use 2.2 % in decimal form, 0.022, to make our calculations easier. p= 2400, r= 0.022, t= 5 Let's now substitute these values into the simple interest formula and evaluate the right-hand side to calculate the amount of interest.
We found that the simple interest over 5 years is $ 264. Now we will calculate the interest for each option one at a time.
Increasing the Interest Rate by 1 %
Let's calculate simple interest for the same principal and time period but with a 1 % higher interest rate. We can write 1 % as a decimal as 0.01.
| Principal, p | Interest Rate, r | Time, t |
|---|---|---|
| 2400 | 0.022 + 0.01 ⟶ 0.032 | 5 |
Let's substitute these values into the simple interest formula and evaluate the right-hand side.
We got that the simple interest over 5 years would be $ 384 if the rate is increased by 1 %. This means that the simple interest earned is $ 384 - $ 264, or $ 120, more if the rate is increased by 1 %. $ 384 - $ 264 = $120
Increasing the Time by 1 Year
This time we will determine what happens with the simple interest if the time is increased by 1 year.
| Principal, p | Interest Rate, r | Time, t |
|---|---|---|
| 2400 | 0.022 | 5 + 1 ⟶ 6 |
Like we did before, we will substitute these values into the simple interest formula and evaluate the right-hand side.
This time, the simple interest is $ 316.80. Let's calculate the difference between the amount of simple interests. 316.80-264=52.80 The simple interest earned is $ 52.80 more if the time is increased by 1 year.
Conclusion
Let's summarize what we have in a table.
| 2.2 % Interest Over 5 Years | 3.2 % Interest Over 5 Years | 2.2 % Interest Over 6 Years |
|---|---|---|
| 264 | 384 | 316.80 |
As we can see, Zosia can earn more interest if the annual interest rate is increased by 1 % than if she received an extra year of interest at the current rate.
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We are asked to find what Zosia's mother will owe the second month if she only pays $ 52 the first month. We know that the first month she has the loan, she owes $ 4500. Then she pays $ 52 for her first payment. Let's calculate her unpaid balance after the first payment. $ 4500- $ 52= $ 4448 After the first payment, her principal unpaid balance is $ 4448. However, each month, 1 % of the unpaid balance is added to the amount she owes. If we add 1 % of $ 4448 to $ 4448, we will get the amount of money that she will owe the second month. Remember that 1 % = 0.01!
If she only pays $ 52 in the first month, she will owe $ 4492.48 in the second month.
Now we want to find what Zosia's mother will owe in the third month if she makes the minimum payment each month. From Part A, we know that if she pays $ 52 the first month, she will owe $ 4492.48 the second month. Let's calculate her unpaid balance after the second payment. $ 4492.48- $ 52= $ 4440.48 After the second payment, her unpaid balance is $ 4440.48. Now let's calculate and add the 1 % interest of this amount to find her total balance, the same way we did in Part A. This will give us her balance going into the third month. Let's do it!
We found that Zosia's mother will owe about $ 4484.88 going into the third month.
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Zosia wants to buy a drone. The regular price of the drone is $640, but the store is offering a discount of 10 % off the regular price. A sales tax of 4.25 % is applied to the discounted price. What is the final price of the drone?
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We want to find the final price of the drone. We will start by calculating the dollar amount of the discount. Let's use the percent equation to do so. part = percent * whole We are given that the regular price of the drone is $ 640. The store is offering a 10 % discount. If we let d represent the dollar amount of the discount, we can write the following equation. d = 10 % * $ 640 We can write the percent as a decimal before we solve the equation. We will do this by ignoring the percent symbol and moving the decimal point two places to the left.
We found that 10 % is equal to 0.10, or 0.1. d = 10 % * $ 640 [0.3em] ⇓ [0.3em] d = 0.1 * $ 640 Finally, let's compute the right-hand side of the equation. We can ignore the units for now for simplicity.
This means that the dollar amount of the discount is $ 64. Now we can calculate the cost after the discount. $640 - $ 64 = $ 576 The discounted price of the drone is $ 576. The final selling price of the drone will be the discounted price plus the sales tax. We are given that a sales tax of 4.25 % is added after the discount. We can find the dollar amount of the sales tax by using the percent equation again. Let t represent the dollar amount of the sales tax. part = percent * whole ⇓ t = 4.25 % * $ 576 We can write the percent as a decimal by ignoring the percent symbol and moving the decimal point two places to the left.
We found that 4.25 % is equal to 0.0425. t = 4.25 % * $ 576 [0.3em] ⇓ [0.3em] t = 0.0425 * $ 576 Now we will solve the equation for t. Let's ignore the units for now.
We found that the dollar amount of the sales tax is $ 24.48. Finally, let's calculate the final selling price by adding the sales tax to the price after the discount. $576 + $ 24.48 = $ 600.48 The final price of the drone is $ 600.48.
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Financial Literacy
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