A share of stock sold for $50 on Monday. On Tuesday it lost 5% of its Monday’s value. On Wednesday it lost 10% of its Tuesday’s value. On Thursday it lost 5% of its Wednesday’s value. What percent increase would the share of stock have to have on Friday to achieve its Monday’s value of $50?
50 * .05 = 2.50
50 - 2.50 = 47.50
47.50 * 0.1 = 4.75
47.50 - 4.75 = 42.75
42.75 * 0.05 = 2.14
42.75 - 2.14 = 40.61
50 - 40.61 = 9.39
9.39/40.61 = 0.2312 = 23.1%
Check my figures.
My answer was 23.1 % also.
To find out the percent increase that the share of stock would have to achieve on Friday to reach its Monday's value of $50, we need to work backward from Thursday. Let's break down the problem step by step.
1. Monday: The stock sold for $50.
2. Tuesday: It lost 5% of its Monday's value. To find out Tuesday's value, we need to subtract 5% of $50 from $50:
Tuesday's value = $50 - (0.05 * $50) = $50 - $2.50 = $47.50.
3. Wednesday: It lost 10% of Tuesday's value. To find out Wednesday's value, we need to subtract 10% of $47.50 from $47.50:
Wednesday's value = $47.50 - (0.10 * $47.50) = $47.50 - $4.75 = $42.75.
4. Thursday: It lost 5% of Wednesday's value. To find out Thursday's value, we need to subtract 5% of $42.75 from $42.75:
Thursday's value = $42.75 - (0.05 * $42.75) = $42.75 - $2.14 = $40.61.
Now, let's find out how much the stock needs to increase on Friday to reach its Monday's value.
5. Friday: The stock needs to achieve its Monday's value of $50. Let's represent the required percent increase as "x." The equation would be:
Thursday's value * (1 + (x / 100)) = Monday's value.
Plugging in the values:
$40.61 * (1 + (x / 100)) = $50.
We can now solve for "x":
(1 + (x / 100)) = $50 / $40.61.
(1 + (x / 100)) = 1.2312. (rounded to four decimal places)
Subtracting 1 from both sides:
x / 100 = 1.2312 - 1.
x / 100 = 0.2312.
Multiplying both sides by 100:
x = 0.2312 * 100.
x = 23.12.
Therefore, the share of stock would need to increase by approximately 23.12% on Friday to achieve its Monday's value of $50.