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Finance The following data represent the amount of money
Chapter 4, Problem 40E(choose chapter or problem)
Problem 40E
Finance The following data represent the amount of money an investor has in an investment account each year for the last6 years. The theory of finance states that account values grow exponentially over time.
Year, x |
Value of Account, y |
Year, x |
Value of Account, y |
0 |
$20,000 |
4 |
$27,484 |
1 |
$21,516 |
5 |
$30,053 |
2 |
$23,355 |
6 |
$32,622 |
3 |
$24,885 |
|
|
(a) Draw a scatter diagram treating time as the explanatory variable.
(b) Determine the logarithm of the y-values so that Y = log y. Draw a scatter diagram of the transformed data.
(c) Find the least-squares regression line of the transformed data.
(d) Find the exponential equation of best fit.
(e) Use the exponential equation of best fit to predict the value of the account after 30 years.
(f) If we subtract 1 from the base, b, in the exponential equation of best fit, we obtain the average annual rate of return on the investment. What was the average rate of return on this investment over the past 7 years?
Questions & Answers
QUESTION:
Problem 40E
Finance The following data represent the amount of money an investor has in an investment account each year for the last6 years. The theory of finance states that account values grow exponentially over time.
Year, x |
Value of Account, y |
Year, x |
Value of Account, y |
0 |
$20,000 |
4 |
$27,484 |
1 |
$21,516 |
5 |
$30,053 |
2 |
$23,355 |
6 |
$32,622 |
3 |
$24,885 |
|
|
(a) Draw a scatter diagram treating time as the explanatory variable.
(b) Determine the logarithm of the y-values so that Y = log y. Draw a scatter diagram of the transformed data.
(c) Find the least-squares regression line of the transformed data.
(d) Find the exponential equation of best fit.
(e) Use the exponential equation of best fit to predict the value of the account after 30 years.
(f) If we subtract 1 from the base, b, in the exponential equation of best fit, we obtain the average annual rate of return on the investment. What was the average rate of return on this investment over the past 7 years?
ANSWER:
Answer
Step 1 of 6
(a)
The following data represent the amount of money an investor has in an investment account each year for the last 6 years.
Year, x |
Value of Account, y |
Year, x |
Value of Account, y |
0 |
$20,000 |
4 |
$27,484 |
1 |
$21,516 |
5 |
$30,053 |
2 |
$23,355 |
6 |
$32,622 |
3 |
$24,885 |
|
|
We are asked to draw a scatter diagram treating time as the explanatory variable.
We can easily plot the scatter diagram using the Microsoft Excel.
