INVESTIGATION: Saving money

Objectives

• To visualize arithmetic and geometric sequences in real life.
• To apply knowledge about arithmetic and geometric sequences to choose the most effective way to save money.

Materials

• Paper
• Pens of different colors
• Calculator
• Internet 

Procedure

Sequences and series can be used to describe many real world situations. One major application of sequences and series is in finances. In this investigation we will investigate two different methods to saving money from a paycheck. 

1. Decide on an item you would like to save up your money for. This item should be worth at least 200 dollars.
2. Suppose you have a job that pays you 100 dollars a week. When you get paid at the end of each week you add a certain amount of money to your savings account.
3. For the first money saving method, decide on an amount of money that you would like to save from your paycheck each week. You can save up to half of your paycheck.
4. Create a table to show how much money you have at the end of each week using this saving method. Stop this table when you have reached or exceeded the amount of money you need to purchase your chosen item.
   

   Sample Table

5. For the second saving method, pick a number from 1-10. This will be your new starting amount of money saved.
6. Choose another number between 2 and 4. This will be the number that you multiply the amount of money saved by at the end of every week.
7. Create a table to show how much money you have at the end of each week using this saving method. Stop this table when you have reached or exceeded the amount of money you need to purchase your chosen item.
   

   Sample Table

Questions

1. Which saving method saved money faster? Why?
2. What type of sequence does the first saving method represent? How do you know?
3. What type of sequence does the second saving method represent? How do you know? 
4. Create a graph of the sequence generated by the first saving method.
5. On the graph that you just created, graph the sequence generated by the second saving method in a different colored pen.
6. Find the sum you are adding into the savings amount each week in the second saving method. Can you afford to add that money in every week with your earnings of 100 dollars a week?
7. How much money would you need to put into your savings on week 6 using the first savings method? Is this plausible given you make 100 dollars a week? 
8. How much money would you need to put into your savings on week 6 using the second savings method? Is this plausible given you make 100 dollars a week?
9. Which saving method would you choose? Explain.
10. Compare with a friend. What method did they choose? Why did they choose that plan? How many weeks of that savings plan did it take them to afford their chosen item?