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Lesson 4

1. Lesson 4

1.11. Explore 7

Mathematics 20-1 Module 1

Module 1: Sequences and Series

 

Try This 5

 

This shows two children rolling a snowball towards the edge of a steep hill. The snowball has a dollar sign on it.

Go to your course folder and retrieve your work from Lesson 2 Try This 1. In that exercise you investigated the investment of $1000 in a savings bond that pays 4% simple interest at the end of every year. The investment earned $40/yr. The value of the investment at the end of each year formed an arithmetic sequence.

 

In the video Deriving a Formula for Compound Interest, you solved a problem involving the investment of $1000 in a savings bond that pays 4%/yr compounded annually. The value of the investment at the end of each year formed a geometric sequence.

  1. In what ways are these problems similar? In what ways are they different?
  1. In Lesson 2 Try This 2, you created a graph relating the value of the investment over the first 10 yr. Create a new graph relating the value of the compound-interest investment over the first 10 yr.
  1. What conclusions can you draw about compound interest as compared to simple interest?
  1. Which investment, the investment with simple interest or the investment with compound interest, is worth more at the end of 10 yr? By approximately how much? hint

This shows a graph of simple interest versus compound interest. The amount of a $1000 investment after 10 years is $1400 in the simple interest case while it is approximately $1480.24 in the compound interest case.