1. Lesson 2

1.10. Explore 6

Mathematics 30-2 Module 7

Module 7: Exponents and Logarithms

 

 

There are different applications that use exponential functions. One of these areas is banking and finance. In Try This 4 you will use exponential equations to calculate investment values.

 

Try This 4

 

This is a photo of a piggy bank on top of a pile of pennies and 20-dollar bills.

iStockphoto/Thinkstock

Are you saving money for something special? You might make that money grow faster if you invest it at a bank or with an investment firm. To calculate how much money you could accumulate, there are some formulas you can use that are based on exponential equations.

  1. Arthur invests $1000 at a rate of 3% per year. This means he will earn 3% of the amount in the account each year. Complete a table like the one that follows to to see how much money Arthur will accumulate after 6 years.1

    3% COMPOUND INTEREST PER YEAR
    Year Starting Value Ending Value
    0 $1000.00 $1000.00 + 0.03($1000.00) = $1030.00
    1 $1030.00 $1030.00 + 0.03($1030.00) = $1060.90
    2 $1060.90 $1060.90 + 0.03($1060.90) = $1092.73
    3    
    4    
    5    
    6    
  2. As you may have noticed from the table in question 1, the interest in year 2 is calculated not only on $1000 but also on the interest earned in year 1. That is why the interest is considered compounded. When you earn interest on principal and preceding interest earned, your money grows faster.

    Instead of using a table to calculate the compound interest, you can use the compound interest formula.

    The formula for compound interest is A = P(1 + i)n, where A is the amount of money at the end of the investment term; P is the principal, the original amount invested; i is the interest rate per compounding period, expressed as a decimal; and n is the number of compounding periods. The compounding period is the time during which interest is calculated on an investment.

    Use this formula to confirm your answer for year 6 in the table from question 1.
  3. Use the compound interest formula to calculate what the value of Arthur’s investment will be after 10 years and after 20 years. Add these values to your chart.
  4. Graph your compound interest formula.
  5.  
    1. Use your graph to determine the amount of time for the investment to grow to $2000.
    2. Describe a method that you could use to answer question a. without using an exponential function. How long would this method take?

course folder Save your responses in your course folder.

 

1 From PRINCIPLES OF MATHEMATICS 12 by Canavan-McGrath et al. Copyright Nelson Education Ltd. Reprinted with permission.