QuestionA man has stock worth \$2800. It drops by 8% and then gains 8% back. What is the stock's value after two days?

Studdy Solution

STEP 1

Assumptions1. The initial value of the stock is $2800. The stock first drops by8% in value3. The stock then gains8% in value from its new value

STEP 2

First, we need to calculate the value of the stock after it drops by8%. We can do this by multiplying the initial value by the percentage drop.
$Value\, after\, drop = Initial\, value \\times (1 - Percentage\, drop)$

STEP 3

Now, plug in the given values for the initial value and percentage drop to calculate the new value.
$Value\, after\, drop = \$2800 \\times (1 -8\%)$

STEP 4

Convert the percentage to a decimal value.
$8\% =0.08$ $Value\, after\, drop = \$2800 \\times (1 -0.08)$

STEP 5

Calculate the value of the stock after the drop.
$Value\, after\, drop = \$2800 \\times (1 -0.08) = \$257$

STEP 6

Next, we need to calculate the value of the stock after it gains8% from its new value. We can do this by multiplying the new value by the percentage gain.
$Final\, value = Value\, after\, drop \\times (1 + Percentage\, gain)$

STEP 7

Now, plug in the values for the value after the drop and the percentage gain to calculate the final value.
$Final\, value = \$2576 \\times (1 +\%)$

STEP 8

Convert the percentage to a decimal value.
$8\% =0.08$ $Final\, value = \$2576 \\times (1 +0.08)$

STEP 9

Calculate the final value of the stock.
$Final\, value = \$2576 \\times ( +.08) = \$2782.08$ The stock is valued at $2782.08 at the end of the second day.

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