If the closing price of Stock Y was $38.63 on Friday, which was after it had earned daily returns of 8.0%, 23.0%, -30.0%, 20.0%, and -5.0% during the week (Monday to Friday), what was the opening price of Stock Y on Monday?
A)$17.47
B)$17.75
C)$33.00
D)$36.44

Question

Quizplus · Accepted Answer

To solve this problem, we need to work backwards from the closing price on Friday using the daily returns.

Let X be the opening price on Monday. Then we have:

Friday's closing price = $38.63 = X * (1 + 8%) * (1 + 23%) * (1 - 30%) * (1 + 20%) * (1 - 5%)

Simplifying this equation, we get:

38.63 = X * 0.86 * 1.23 * 0.7 * 1.2 * 0.95

38.63 = X * 0.568914

X = $68 / 1.86914 = $36.44

Therefore, the opening price of Stock Y on Monday was $36.44 (option D).

If the Closing Price of Stock Y Was $38