Chapter 4.2, Problem 26E

Solution

To describe: The error in writing a model for the value of the stock after t years.

The error in calculation was that the wrong factor $\left(\frac{2}{100}\right)$ was used instead of correct factor $\left(1-\frac{2}{100}\right)$ .The correct modelling of the stock value is $S\left(t\right)=\text{500}{\left(0.98\right)}^t$

Given data: A person invested $500 in the stock of a company. The value of stock decreases 2% each year. The calculations for model shown in Fig.1.

  

Method/Formula used:

The correct formula for the evaluation of stock after time t when rate of decrease of the stock is r % is given by

  $S\left(t\right)=\left(\text{Initial}\text{amount}\right){\left(1-r\%\right)}^t$

Calculations:

The initial amount of the stock is $500 and decay rate 2% per year. The value of stock after t years is

  $\begin{array}{c}S\left(t\right)=\text{500}{\left(1-\frac{2}{100}\right)}^t\\ =\text{500}{\left(0.98\right)}^t\end{array}$

Thus, the error in calculation was that the wrong factor $\left(\frac{2}{100}\right)$ was used instead of correct factor $\left(1-\frac{2}{100}\right)$ .

The correct modelling of the stock value is

  $\begin{array}{c}S\left(t\right)=\text{500}{\left(1-\frac{2}{100}\right)}^t\\ =\text{500}{\left(0.98\right)}^t\end{array}$