Sign In
| 9 Theory slides |
| 9 Exercises - Grade E - A |
| Each lesson is meant to take 1-2 classroom sessions |
Here are a few recommended readings before getting started with this lesson.
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.
How much tip did they leave?
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.
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.
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 |
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.
Substitute values
Write as a decimal
Multiply
Substitute values
Multiply
LHS/20000=RHS/20000
ba=b/100a/100
Write as a decimal
Convert to percent
Rearrange equation
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?Calculate the total cost using the methods described by Vincenzo and the salesperson. Use the percent equation to calculate the amount of the tax.
p=7, w=120
a%=100a
ca⋅b=ca⋅b
Calculate quotient
Write as a sum
Distribute 120
Multiply
Add terms
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=10.00, w=34.00
Rearrange equation
LHS/34.00=RHS/34.00
Use a calculator
Convert to percent
Round to nearest integer
a=44.00, p%=120%
a%=100a
ca⋅b=ca⋅b
LHS⋅100=RHS⋅100
LHS/120=RHS/120
Calculate quotient
Round to 2 decimal place(s)
Rearrange equation
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?Calculate the total amount of money that she earns in twenty-four months, then calculate 8% of that amount.
p=8, w=28800
a%=100a
ca⋅b=ca⋅b
Split into factors
Cancel out common factors
Simplify quotient
Multiply
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%=100a
ca⋅b=ca⋅b
Multiply
Calculate quotient
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.
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
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.
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.
Zosia's mother used her credit card to purchase a vacation package worth $4500 for the upcoming summer. The monthly minimum payment is $52. Each month, 1% of the unpaid balance is added to the amount she owes.
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.
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.