1. Lesson 6

1.7. Explore 6

Mathematics 30-2 Module 7

Module 7: Exponents and Logarithms

 

When a problem is modelled using an exponential equation, it is often useful to solve that equation using logarithms. In Try This 4, you will solve a problem involving compound interest.

 

Try This 4

 

This photo shows a piggy bank standing on a trail of bills of various denominations.

iStockphoto/Thinkstock

When a bank sets a rate for an investment or a loan in Canada, the prime rate set by the Bank of Canada is often used as a guideline. In 1981, the prime rate reached 22.75%, and, in 2009, it dipped to 2.25%. Compare the time it takes an investment to increase using these two rates by completing the following questions.

  1. Imagine depositing $1000 into a bank account that paid compound interest at 2.25% per year and $1000 into one that paid 22.75% per year. Write an exponential equation to represent the amount of money in each account after t years.
  2. How much money would each account have after 5 years?
  3. Determine how long it would take for each account to accumulate $5000 by solving the equations using logarithms.
  4. Typically, extreme interest rates like these don’t last for very long. How would this change your expectation for the length of time taken for $1000 to grow into $5000?

course folder Save your responses in your course folder.


For the 22.75% account, you should begin with A = 5000(1.2275)t.
For the 2.25% account, you should have A = 1000(1.0225)t.