Thats Interesting

• ## 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?

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

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

4. 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?

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.

• 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?