Bill wants to give Maria a $630,000 gift in 3 years. If money is worth 6% compounded semiannually, what is Maria's gift worth to
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Answer:
1. That values that you must plot are:
- (1, 4.08))
- (20, 5.08)
- (40, 6.18)
2. Yes, the plot of those three points is straight enough.
Explanation:
<em><u>A. What are the values you will plot? </u></em>
The x-ccordinate of your plot is still the number of years the exmployees have worked for the company.
The y-coordinate of your plot is the the base-10 logarithm of the salary.
Therefore:
<u>1) A part-time shipping clerk</u>: 1 year, $12,000
⇒
<u>2) A manager</u>: 20 years, $120,000
⇒
<u>3) The CEO</u>: 40 years ago, $1,500,000
⇒
Summarizing, the points to plot are:
- (1, 4.08)
- (20, 5.08)
- (40, 6.18)
<u><em>B. Will the plot of these three points be straight enough?</em></u>
To find whether the plot is straight enoguh, you may either plot them, make a regression, or, since they are only three points, you can whether the change of rate of the points is constant.
- <u>Change of rate of the first two points, r</u>:
r = rise/run = Δy / Δx = (5.08 - 4.08) / (20 - 1) =1.00/19 ≈ 0.05
- <u>Change of rate of the second and the third points, r</u>:
r = rise/run = Δy / Δx = (6.18 - 5.08) / (20 - 1) = 0.05
Since both rate of changes are equal (or reasonably equal) the plot is straight enough.