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Thats Interesting

  • Classroom Resources / Problems of the Week

    Thats Interesting


    PoW ID: 4684

    Problem Print

    On December 31, 2007, Curtis and Bill each had $1000 to start saving for retirement. The two men had different ideas about the best way to save, though.

    Curtis, who doesn't trust banks, put his money in a can and buried it in his back yard. He plans to continue adding $1000 to the can on the last day of each year until he is ready to retire.

    Bill invested his $1000 in a bank account that will pay 10% interest annually on the last day of the year. Unlike Curtis, he does not plan to continue investing more money each year. He figures that with the interest he will earn his bank account will eventually be worth more than the money in Curtis's can.

    1. How much money will each man have on January 1, 2009?

    3. How much money will each man have on January 1, 2010?

    5. Write a variable expression for each man that represents how much money he will have x years after January 1, 2008.

    7. Will Bill's bank account ever be worth more than the money Curtis has collected in his can? How do you know?

    Extra

    Extra: Suppose that instead Bill had invested $2000 and Curtis had buried $500 on December 31, 2007. If Bill invests no more money and Curtis continues to bury $500 each year, for what calendar years would Curtis have more money on January 1st? How do you know?

    Answer Check

    Show Answer

    On January 1, 2009, Bill has $1100 and Curtis has $2000. On January 1, 2010, Bill has $1210 and Curtis has $3000. Be sure that you've also answered questions 3 and 4 and explained clearly how you came up with your answers.

    If your answers don't match ours,

    • did you understand that on January 1, 2009 Curtis has just buried another $1000 the day before on December 31, 2008?
    • did you remember that each year Bill earns 10% of his current account value, not just another 10% of the original $1000?
    • did you understand that if x is the number of years after January 1, 2008, then x = 1 in 2009, x = 2 in 2010, and so on?
    • did you try making a chart to look for patterns in how much money each man has each year?
    • did you try graphing your expressions or equations?
    • did you check your math?
    If any of those ideas helps you, you might revise your answer, and then leave a comment that tells us what you did. If you're still stuck, leave a comment that tells us where you think you need help.

    If your answer does match ours,

    • did you use algebraic techniques to find your answer?
    • did you show and explained the work you did?
    • is your explanation clear and complete? Would another student understand your solution?
    • did you make any mistakes along the way? If so, how did you find and fix them?
    • are there any hints that you would give another student?
    • did you try the extra?
    Revise your work if you have any ideas to add. Otherwise leave us a comment that tells us how you think you did - you might answer one or more of the questions above.