GM Lesson 017 Simple Interest

Learning Intentions

By the end of this lesson, students will be able to:

• Use the simple interest formula .
• Identify principal, interest rate and time in simple interest problems.
• Calculate simple interest and final amount in practical contexts.

Prerequisites

Students should already be able to:

• Convert percentages to decimals, such as .
• Calculate percentages of quantities.
• Substitute values into a formula.
• Convert months into years.
• Add money amounts and round to the nearest cent where needed.

Key Idea Summary

Simple interest is interest calculated only on the original amount of money.

The simple interest formula is:

where:

• is the simple interest earned or charged.
• is the principal, which is the original amount of money.
• is the annual interest rate written as a decimal.
• is the number of years.

The final amount is:

where is the total amount after interest has been added.

To solve a simple interest problem:

1. Identify , and .
2. Convert the percentage rate to a decimal.
3. Convert the time to years if needed.
4. Substitute into .
5. Find the final amount using .

Direct Instruction and Worked Examples

Time Allocation

Time Allocation

Time Allocation

• Introduction, warmup and vocabulary: 5 minutes
• Direct instruction: 15 minutes
• Understanding checks: 5 minutes
• Exercises: 20 minutes
• Homework: 20 to 30 minutes outside the lesson it was taught in.

Link to original

Direct Instruction

Simple interest is used when interest is calculated only on the original principal.

For example, if $ is invested at simple interest per year for years, the interest is calculated from the original $ each year.

The interest does not earn extra interest.

The annual interest rate must be written as a decimal:

So for $ at per year for years:

The formula is:

After calculating the interest, the final amount is found using:

Worked Example 1: Calculating Simple Interest

A student invests $ in a savings account paying simple interest per year for years. Calculate the simple interest earned.

Identify the values:

Substitute into the formula:

The simple interest earned is $ .

Worked Example 2: Calculating the Final Amount

A person borrows $ at simple interest per year for years. Calculate the interest charged and the final amount owed.

Identify the values:

Calculate the interest:

Calculate the final amount:

The interest charged is $ , and the final amount owed is $ .

Worked Example 3: Time Given in Months

A bike shop offers a payment plan where $ is borrowed at simple interest per year for months. Calculate the total amount to be repaid.

Convert the time to years:

Identify the values:

Calculate the interest:

Calculate the final amount:

The total amount to be repaid is $ .

Worked Example 4: Finding the Principal

An account earns $ simple interest after years at an annual simple interest rate of . Find the principal.

Start with the formula:

Identify the values:

Substitute:

Solve for :

The principal was $ .

Understanding Checks

Check 1

A bank account pays simple interest per year.

What decimal value should be used for ?

Check 2

For the formula , identify , and in this situation:

A person invests $ at simple interest per year for years.

Check 3

A loan of $ is charged simple interest at per year for years.

Without fully solving, explain whether the final amount will be greater than, less than or equal to $ .

Check 4

A simple interest problem gives the time as months.

What value of should be used in the formula ?

Check 5

Explain the difference between the interest and the final amount .

Exercises

Simple Familiar Exercises

Exercise 1

Calculate the simple interest earned on $ invested at per year for years.

Exercise 2

Calculate the simple interest charged on a loan of $ at per year for years.

Exercise 3

An investment of $ earns simple interest at per year for years.

Calculate:

a. the simple interest earned
b. the final amount

Exercise 4

A loan of $ is charged simple interest at per year for years.

Calculate:

a. the interest charged
b. the total amount to be repaid

Exercise 5

Calculate the simple interest on $ at per year for months.

Complex Familiar Exercises

Exercise 6

A student saves $ in an account paying simple interest per year for months.

Calculate:

a. the time in years
b. the simple interest earned
c. the final amount in the account

Exercise 7

A small business borrows $ at simple interest per year for months.

Calculate:

a. the interest charged
b. the total amount owed

Exercise 8

A person invests $ in one account at simple interest per year for years.

They invest another $ in a different account at simple interest per year for years.

Calculate the difference between the two final amounts.

Exercise 9

A loan has a principal of $ and earns simple interest of $ after years.

Use the formula to find the annual interest rate as a percentage.

Exercise 10

An investment earns $ simple interest over years at an annual rate of .

Find the principal.

Homework Problems

Problem 1

Calculate the simple interest on $ at per year for years.

Problem 2

Calculate the final amount for an investment of $ at simple interest per year for years.

Problem 3

A loan of $ is charged simple interest at per year for months.

Calculate:

a. the time in years
b. the interest charged
c. the total amount to be repaid

Problem 4

An investment earns $ simple interest after years at per year.

Find the principal.

Problem 5

A person borrows $ and repays $ after years under simple interest.

Find:

a. the interest paid
b. the annual simple interest rate

Problem 6

Two payment plans are offered for a motor scooter with a cash price of $ .

Plan A charges simple interest per year for years.

Plan B charges simple interest per year for years.

Calculate the total repayment for each plan and decide which plan is cheaper.

Next: GM Lesson 018 Currency Exchange Rates