Chapter 1.1, Problem 61E

Solution

a)

To find: The month in which both A and L bought the stock.

Both A and L bought the stock in March.

Given Information:

The graph shown in figure 1.

  

Figure 1

Explanation:

There is an increase in the price from $\$100$ to $\$120$ between February and March.

Therefore, both A and L would have bought the stock in March.

b)

To find: The approximate price at which A and L bought the stock.

Both A and L bought the stock at the price of $\$120$ .

Given Information:

The graph shown in figure 1.

  

Figure 1

Explanation:

From the graph in figure 1, it follows that in March the stock price was $\$120$ .

Therefore, both A and L bought the stock at the price of $\$120$ .

c)

To find: When did A sell the stock.

A sold the stock in June.

Given Information:

According the A’s rule, if the stock doesn’t perform well for consecutive three months, then the person will sell the stock.

Explanation:

From the graph, it follows that from March, the prices of the stock fell continuously for three months.

Therefore, A sold the stock in June.

d)

To find: How much A loses on the stock.

A lose $\$2000$ on the stock.

Given Information:

A bought 100 shares at the price $\$120$ .

Explanation:

A sold the shares at $\$100$ so he earned $\$100\times \$100=\$10000$ .

A bought 100 shares at the price $\$120$ so he invested $\$120\times \$100=\$12000$ .

The amount he lost is $\$12000-\$10000=\$2000$ .

Therefore, A’s total loss is $\$2000$ .

e)

To explain: Why Person L’s strategy was better for this particular stock and year over Person A’s strategy.

Given Information:

The graph shown in figure 1. Also, according the A’s rule, if the stock doesn’t perform well for consecutive three months, then the Person A will sell the stock, and according to Person L’s rule if the stock doesn’t perform well since its purchase, then Person L will sell the stock in December.

Explanation:

A sold his stock in March and since then the price of the stock is started rising again. At the end of the year, it rises to $\$140$ .

Now, L sold her stock at the end of the year.

So, she got $\$140\times \$100=\$14000$ .

She invested $\$120\times \$100=\$12000$ .

Thus, she earned a profit of $\$14000-\$12000=\$2000$ .

Since L earned a profit of $\$2000$ and A lost $\$2000$ it implies that L’s strategy worked well for her than A’s strategy for that particular year.

f)

To sketch: A 12-month graph of a stock’s performance that would favor A’s strategy over L’s.

Given Information:

According the A’s rule, if the stock doesn’t perform well for consecutive three months, then the Person A will sell the stock, and according to Person L’s rule if the stock has failed to perform well since its purchase, then Person L will sell the stock in December.

Graph:

Person A’s strategy would be favoured if any graph decrease steadily from March to December.

The graph in figure 2 shows that A’s strategy is better than L’s.

  

Figure 2

In this case, L sold her stock at the end of the year.

So, she got $\$100\times \$100=\$10000$ .

A sold his stock in July at $\$110$ . So, he earned $\$110\times \$100=\$11000$ .

Thus, A earned more than L.