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Simple Interest, Tax, Commissions




 

Video solutions to help Grade 7 students learn how to solve simple interest problems using the formula
I = Prt and solve percent problems involving tax, gratuities, commissions, and fees.


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Lesson Plans and Worksheets for Grade 7

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More Lessons for Grade 7

Common Core For Grade 7

New York State Common Core Math Grade 7, Module 4, Lesson 10


Lesson 10 Student Outcomes


• Students solve simple interest problems using the formula I = Prt, where I = interest, P = principal, I = interest, r = rate, and t = time.
• When using the formula I = Prt, students recognize that units for both interest rate and time must be compatible; students convert the units when necessary.

Lesson 11 Student Outcomes


• Students solve real-world percent problems involving tax, gratuities, commissions, and fees.
• Students solve word problems involving percent using equations, tables, and graphs.
• Students identify the constant of proportionality (tax rate, commission rate, etc.) in graphs, equations, tables, and in the context of the situation.

Lesson 10 Classwork

Interest = Principal x Rate x Time
I = P x r x t
I = Prt
• r is the percent of the principal that is paid over a period of time (usually per year).
• t is the time.
• r and t must be compatible. For example, if r is an annual interest rate, then t must be written in years.

Example 1: Can Money Grow? A Look at Simple Interest
Larry invests in a $100 savings plan. The plan pays 4 1/2% interest each year on his account balance.
a. How much money will Larry earn in interest after 3 years? After 5 years?
b. How can you find the balance of Larry’s account at the end of years?

Example 2: Time Other Than One Year
A savings bond earns simple interest at the rate 3% of each year. The interest is paid at the end of every month. How much interest will the bond have earned after three months?

Example 3: Solving for P, r, or t.
Mrs. Williams wants to know how long it will take an investment of $450 to earn $200 in interest if the yearly interest rate is 6.5% paid at the end of each year.



Lesson 11 Classwork

Opening Exercise
How are each of the following percent applications different, and how are they the same? First, describe how percents are used to solve each of the following problems. Then, solve each problem. Finally, compare your solution process for each.
a. Silvio earns 10% for each car sale he makes while working at a used car dealership. If he sells a used car for $2000, what is his commission?
b. Tu’s family stayed at a hotel for nights on their vacation. The hotel charged a 10% room tax, per night. How much did they pay in room taxes if the room cost per night?
c. Eric bought a new computer and printer online. He had to pay 10% in shipping fees. The items totaled $2000. How much did the shipping cost?
d. Selena had her wedding rehearsal dinner at a restaurant. The restaurant’s policy is that gratuity is included in the bill for large parties. Her father said the food and service were exceptional, so he wanted to leave an 10% extra tip on the total amount of the bill. If the dinner bill totaled $2000, how much money did her father leave as the extra tip?


 
Lesson 10 Exercise 1
Find the balance of a savings account at the end of 10 years if the interest earned each year is 7.5%. The principal is $500.
Exercise 2
Write an equation to find the amount of simple interest, A, earned on a $600 investment after 1 1/2 years if the semi-annual (six month) interest rate is 2%.

Exercise 3
A $1,500 loan has an annual interest rate of 4 1/4 % on the amount borrowed. How much time has elapsed if the interest is now $127.50?


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