Word Problems: Stock Price: Example 1

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Let's look at the daily fluctuations of stock prices. ("Start", "starting", "open", and "opening" all refer to the beginning of a business day.)
If a stock starts day 1 at $100, but loses 3% on that day, at what percent of $100 will it start day 2?

On day 2, it will start at 100 – 3 = 97% of $100..

Express this with a decimal.

On day 2, the price will start at 0.97 * $100, or $97.

If the stock gains 5% during day 2, express its price at the beginning of day 3 in terms of a percentage of the day 2 opening price of $97.

At the start of day 3, the price will be 105% of $97.

Express the day 3 opening price in terms of a decimal multiplied by the day 2 opening price.

(day 3 opening price) is 1.05 * (day 2 opening price).

Use these two decimals to express the (day 3 opening price) in terms of the (day 1 opening price).

(day 3 opening price) = 0.97 * 1.05 * (day 1 opening price), or (day 3 opening price) = $101.85. Notice that neither decimal represents the data of 3% and 5%, but that they are related to those values: 1) after a 3% loss, we use 100% – 3% = 97%. 2) after a 5% gain, we use 100% + 5% = 105%.

Use these ideas on $50 stock which gains 2% on day 1 and loses 4% on day 2.

Express the day 3 opening price of this second stock in terms of its day 1 opening price.

(day 3 opening price) = 1.02 * 0.96 * 50 = $48.96.

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