3.2+Investing+for+the+Future

12-10-08** Big Idea: The rate at which things grow or decay can often be described mathematically. Essential Question: How can I show a pattern of repeated division? __Problem 3.2 Investing for the future
 * YMJ

A.__ 10 4223.697398
 * Year || The value of the collection ||
 * 1 || 2500 ||
 * 2 || 2650 ||
 * 3 || 2809 ||
 * 4 || 2977.54 ||
 * 5 || 3156.1924 ||
 * 6 || 3345.563944 ||
 * 7 || 3546.297781 ||
 * 8 || 3759.075647 ||
 * 9 || 3984.620186 ||

__**B.**__ Year 1 = n 2650/2500 = 1.06

Year 2 = n 2809/2650 = 1.06

Year 3 = n 2977.54/2809 = 1.06

Year 4 = n 3156.1924/2977.54 = 1.06

Year 5 = n 3345.563944/3156.1924 = 1.06

Year 6 = n 3546.297781/3156.1924 = 1.06

Year 7 = n 3759.075647/3546.297781 = 1.06

Year 8 = n 3984.620186/3759.075647 = 1.06

Year 9 = n 4223.697398/3984.620186 = 1.06

Year 10 = n 4477.119241/4223.697398 = 1.06


 * __C.1__**
 * Year || The value of the collection ||
 * 1 || 2600 ||
 * 2 || 2704 ||
 * 3 || 2812.16 ||
 * 4 || 2924.6464 ||
 * 5 || 3041.632256 ||
 * 6 || 3163.297546 ||
 * 7 || 3289.829448 ||
 * 8 || 3421.422626 ||
 * 9 || 3558.279531 ||
 * 10 || 3700.610712 ||
 * __C.2__**

Year 1 = n 2600/2500 =1.04 Year 2 = n 2704/2600 = 1.04 Year 3 = n 2812.16/2704 Year 4 = n 2924.6464/2812.16 = 1.04 Year 5 = n 3041.632256/2924.6464 = 1.04 Year 6 = n 3163.297546/3041.632256 = 1.04 Year 7 = n 3289.829448/3163.297546 = 1.04 Year 8 = n 3421.422626/3289.829448 = 1.04 Year 9 = n 3558.279531/3421.422626 = 1.04 Year 10 = n 3700.610712/3558.279531 = 1.04

__**D.**__ 100%+ 5% = 105% 105% = 1.05 1.05 is the growth factor


 * __Prblem 3.2 Follow-up__**

1. value= 100% of this year's value + 6% of this year's value = 106% of this year's value = 1.06 x this year's value The growth factor is 1.06.

2. For 4%

= 104% of this year's values = 1.04 x this year's values The growth factor is 1.04.

For 5%

= 105% of this year's values =1.05 x this year's values The growth factor is 1.05.

3. 2500(1.06^t) for t

t= 1 v = 2500(1.06¹) v = 2500 x 1.06 v = 2050

t = 2 v = 2500(1.06²) v = 2500 x 1.1236 v = 2809