Home work: For some of you this graphing process is quite foreign, so we have altered exercise #9 to allow you more practice. Exercise #9 on page 825 uses the rule of 72 to estimate the doubling time of an account paying annual interest compounded yearly (This only works for accounts which are compounded yearly):
For example if you bank offers you an account which pays 3% annual interest compounded yearly, then you doubling time would be about 72/(100*.03) = 72/3, or 24 years. You can do far better than this approximation. You can calculate the exact doubling time using your graphing calculator. For exercise #9 a, b, & c, I want you to use the rule of 72 to estimate the doubling time and then use your graphing calculator to find the exact doubling time. To show your work you should write down what you typed in for y1 and y2, indicate your window range (x-range (xMin, xMax), y-range (yMin, yMax)), and sketch your view window. While working through part a, b, & c, fill in the following chart:
rate |
Approx. doubling time (Rule of 72) |
Amount at this time |
Actual doubling time |
3% |
24 years |
1000(1+.03/1)^(24*1) = ? |
use graphing calc |
4% |
|||
6% |
|||
8% |
|||
9% |
|||
12% |
|||
24% |
|||
36% |
Finally use this chart to do #9 part d: discuss your conclusions about the rule of 72. (For what rates is the rule more accurate and for what rates is it least accurate?)