body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

{{ 'ml-label-loading-course' | message }}

{{ toc.name }}

{{ toc.signature }}

{{ tocHeader }} {{ 'ml-btn-view-details' | message }}

{{ tocSubheader }}

{{ 'ml-lesson-btn-finish-worksheet' | message }}

{{ 'ml-toc-proceed-mlc' | message }}

{{ 'ml-toc-proceed-tbs' | message }}

An error ocurred, try again later!

Chapter {{ article.chapter.number }}

{{ article.number }}.

{{ article.displayTitle }}

{{ article.intro.summary }}

Show less Show more

{{ ability.displayTitle }}

Lesson Settings & Tools

	{{ 'ml-lesson-number-slides' \| message : article.intro.bblockCount }}
	{{ 'ml-lesson-number-exercises' \| message : article.intro.exerciseCount }}
	{{ 'ml-lesson-time-estimation' \| message }}

{{ item.file.title }}
{{ presentation }}

No file copyrights entries found

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.

Percent
Proportion
Ratio
Percent Proportion
Percent Equation
Percent of Change

Challenge

Leaving a Tip

Vincenzo went out for dinner together with his family. The total cost of the meal was Because they really enjoyed the food and the service, they left a tip.

Error loading image.

How much tip did they leave?

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

simple interest per year on a deposit of

This means that the simple interest earned on

in one year is

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

simple interest each year.

Years	Amount of Simple Interest	Balance

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 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 in this account as principal.

After talking with several bankers, he notices that banks offer different interest rates.

a If the bank offers

simple interest per year, what will be the balance after

years?

b If an account earns

in

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

Solution

a Notice that the balance is the final amount of money in the account after adding the interest. The amount of principal is

and the bank offers

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.

In this formula,

is the amount of interest,

is the principal,

is the annual interest rate, and

is the time in years. Since Vincenzo's money will stay in this account for

years, substitute the values

and

into the formula to calculate the total amount of interest.

SubstituteValues

Substitute values

Write as a decimal

Multiply

The account will earn

in

years. As a final step, add this amount to the principal to calculate the final balance in

years.

The balance of the account will be

after

years.

b This time the amount of interest earned in

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.

Substitute these values into the formula and solve for the annual interest rate

SubstituteValues

Substitute values

▼

Solve for

Multiply

Write as a decimal

Convert to percent

Rearrange equation

The bank offers a

annual interest rate.

Example

Who is Correct?

Vincenzo goes to Miami, Florida, to visit his aunt and uncle. The city's sales tax rate is Vincenzo wants to buy a new coat. The price of the coat before tax is Vincenzo says that the total cost can be calculated by finding of and adding this value to

However, the salesperson says that to find the selling price, the price of the coat

needs to be multiplied by

Who is correct?

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

This means that to purchase an item, an additional

of its original price must be paid as sales and use tax.

Calculate the tax for a

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

of

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.

In this equation,

represents the amount of tax,

is the percent, and

is the original price of the item. Substitute the values into the percent equation and calculate

of

Remember to write the percent as a decimal number.

,

MoveRightFacToNum

Calculate quotient

The amount of the tax for a

coat is

Now add this amount to the original price of the coat to find the total cost.

Vincenzo can buy this coat for

Next, calculate the total cost following the salseperson's method.

The salesperson's Way

The salesperson calculates the total cost by multiplying

by

Check the result to see if it is the same as Vincenzo's solution.

Write as a sum

Distribute

Multiply

Add terms

According to the salesperson's calculations, the total cost of the coat is

Conclusion

Notice that both methods gave the same result. This is because multiplying

by

or

and adding the result to

is the same as multiplying

by

Both of the ways are correct and give the same total cost. This means that both Vincenzo and the salesperson are correct.

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.

a Vincenzo received a

discount on the jeans he purchased. What percent discount did he receive on them? Round the answer to the nearest integer.

b A few days later, Vincenzo saw the same shoes on an online shopping platform. He noticed that the price in-store had a

markup compared to the price online. What is the price of the sneakers online? Round the answer to two decimal places.

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

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

and Vincenzo received a discount of

Now, recall the formula for the percent equation.

In the percent equation, the part of the whole

is the percent

multiplied by the whole

Here, the discount of

dollars is the part

the percent is

and the whole

is the original price,

dollars.

,

▼

Solve for

Rearrange equation

Use a calculator

Convert to percent

Round to nearest integer

The discount is equal to about

of the original price.

b Vincenzo noticed that the price of the sneakers in store includes a

markup compared to the price online. To find the price online, start by adding

to

The in-store price of the sneakers is

of the price online. Now, recall the formula for the percent equation once again.

According to the receipt, the in-store price of the sneakers is

This represents the part

The percent is

and the whole

is the price online. Now, solve the equation for

,

▼

Solve for

MoveRightFacToNum

Calculate quotient

Round to decimal place(s)

Rearrange equation

The price of the sneakers is about

on the online platform.

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 of the contract's total value.

If Vincenzo's aunt makes

a month, how much money will she make as a bonus?

Hint

Calculate the total amount of money that she earns in twenty-four months, then calculate of that amount.

Solution

Start by calculating the total value of the contract. Since Vincenzo's aunt earns

per month, multiply this amount by

to find the total amount of money that she earns in two years.

She earns

dollars in two years. Per her contract,

of this amount will be given as a bonus. The percent equation can be used to calculate

of

Recall that the part

is equal to the product of the percent

and the whole

Substitute

and

into the percent equation to find the value of

,

MoveRightFacToNum

SplitIntoFactors

Split into factors

CancelCommonFac

Cancel out common factors

Simplify quotient

Multiply

Vincenzo's aunt will get

as a bonus after working for the company for two years.

Example

Paying Back a Loan

Vincenzo's uncle borrows to repair his car. He will pay off the loan over years by paying back the principal plus simple interest for each year.

a Help Vincenzo's uncle calculate how much money he will pay in interest.

b How much will he pay back altogether?

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.

In this case, the

of the loan is

and the

is

Let the

be represented by

For simplicity, ignore the units for now.

Next, solve the equation for

Remember that percents can be written as decimals by moving the decimal point two places to the left.

Multiply

This means that the simple interest for one year is equal to

Finally, multiply the interest for one year by

to calculate the total amount of interest that Vincenzo's uncle will pay over

years.

Vincenzo's uncle will pay

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,

is the amount of interest,

is the principal,

is the interest rate, and

is the time in years.

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

in total in interest over the four years of the loan.

This means that he will pay

altogether when repaying the loan.

Closure

Calculating the Amount of Tip

The challenge presented at the beginning of the lesson was to find

of

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.

Note that the percent

is

and the total cost of the meal represents the whole, which is

Now substitute these values into the percent equation.

Evaluate the right-hand side of the equation to find the value of

Remember to rewrite the percent as a fraction.

MoveRightFacToNum

Multiply

Calculate quotient

They left a

tip.

{{ grade.displayTitle }}

Edit Lesson

Loading content