1. Lesson 6

1.5. Explore 4

Mathematics 30-1 Module 6

Module 6: Exponents and Logarithms

 

In Try This 4 you will explore how exponential equations can be used to solve problems involving investments and credit cards.

 

Try This 4

 

This is a photo of money tucked into a red envelope.
Hemera/Thinkstock

 

Answer the following questions using the compound interest formula A = P(1 + i)n, where

  • A is the future value
  • P is the present value
  • i is the interest rate per compounding period, as a decimal
  • n is the number of compounding periods

Scenario 1

 

Eoghan (pronounced Ewan) receives a gift of $500 and decides to invest in a GIC (guaranteed investment certificate) that earns 5.5% per year, compounded semi-annually. Determine how long it will take for Eoghan’s GIC to be worth $700 by answering the following questions.

  1. Determine the following variables, and identify the unknown variable.
    • A
    • P
    • i
    • n
  2. Substitute the values from question 1 into the formula A = P(1 + i)n. Solve for the unknown variable.
  3. Use your answer from question 2 to determine how many years it will take for the GIC to be worth $700.

    This is a photo of two students using a tablet computer.
    iStockphoto/Thinkstock

Scenario 2

 

Jia used a credit card to purchase an $850 tablet computer. The interest rate charged on overdue balances is 18% per year, compounded daily. Answer the following questions to determine how many days Jia’s payment is overdue if the amount owed on her credit card is $875.

  1. Use the compound interest formula to determine the following variables. Make sure to identify the unknown variable.
    • A
    • P
    • i
    • n

  2. Substitute the values from question 4 into the formula A = P(1 + i)n. Solve for the number of days the balance is overdue.

  3. Compare the procedures you used to solve questions 2 and 5. What stayed the same and what changed in the two procedures?

course folder Save your responses in your course folder.

 

Did You Know?

This is a photo of different credit cards.

Comstock/Thinkstock

The Diners Club, introduced in 1950, was the first universal credit card. Today, many adults have at least one credit card. In fact, to rent a car, you must have a credit card. There is an element of risk to a financial institution in extending credit to individuals. Many credit cards charge a high interest rate on balances not paid after a month. These interest rates are usually compounded daily.

This is an exponential equation.
Remember i and n depend on the number of compounding periods. The interest on credit cards is compounded daily, so there are 365 compounding periods per year.
This is an exponential equation where there is no common base. Logarithms will be very helpful in this case.
Remember i and n depend on the number of compounding periods. The investment is compounded semi-annually, so there are 2 compounding periods per year.