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# Suppose that a stock’s price

Suppose that a stock’s price is \$48 at the end of Day 1. If the price of the stock increases by 30% during Day 2, 20% during Day 3 and then decreases by 5% during Day 4, what is the total percentage change in the stock price during these 3 days?

### 2 Answers by Expert Tutors

Justin L. | A Personalized Approach to a Standardized EducationA Personalized Approach to a Standardize...
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FIRST OFF --> PERCENT CHANGE IS THE NEW PRICE MINUS THE OLD PRICE DIVIDED BY THE OLD PRICE.  THE OLD PRICE FROM DAY 1 WAS \$48, WE NEED TO FIND OUT THE NEW PRICE.....

DAY 1 48
DAY 2 IS AN INCREASE OF 30%, EASIEST WAY TO DO THAT IS 1.3 X 48 = 62.4
DAY 3 IS AN DECREASE BY 5%  ... SO 62.4 (FROM THE DAY BEFORE) X .95     62.4 X .95 = 59.28

SO 59.28 IS OUR NEW PRICE.

% CHANGE IS (NEW-OLD)/OLD  OR (59.28 -48)/48 = .235 OR 23.5%

.......

HOW DID I GET THE AMOUNTS FOR EACH DAY?????
TO INCREASE OR DECREASE AN AMOUNT BY A GIVEN PERCENT
TAKE THE AMOUNT THAT YOU HAVE AND TIMES IT BY 1 PLUS THE PERCENT AS A DECIMAL....

SO LETS DO ANOTHER EXAMPLE
A GIRL MAKES \$30 AN HOUR, BUT IS GETTING  A 10% RAISE.....
SO DO 30 X 1.1 (1.1 BC 10% IS .10...1+.10 IS 1.1)  = \$33  SINCE SHES GETTING MORE MONEY YOU ADD THE .10

OR

A GIRL BUYS A CAR FOR \$2500, AS SOON AS SHE DRIVES IT OFF THE LOT IT LOSES 15% OF ITS VALUE...
SO DO \$2500 X .85 (1 - .15) = 2125
HOPE THAT HELPS
Dallas N. | Texas Aggie with Biochem degree, focus on math and sciencesTexas Aggie with Biochem degree, focus o...
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Since you're looking for the percentage increase, the stock price is irrelevant.  We just need to focus on the percent changes each day.

A 30% change, as seen from Day 1 to Day 2, can be calculated by multiplying the initial price by 1.3.  (As you may recall, 30% can be displayed in decimal form as 0.3, and 1 + 0.3 = 1.3)

For the second increase, mutliply by 1.2 for a 20% change.

For the third, we multiple by 0.95 (a 5% decrease is the same as 1 - 0.05 which equals 0.95).  You'll notice that all the increases are calculated by calculating a number higher than 1, and a decrease is calculated by multiplying by a number less than 1.

To get the total change, we simoly multiply all three factors together.

1.3 * 1.2 * 0.95 = 1.482, or a 48.2% change.