Question

The value of a stock is decreasing exponentially at a rate of 18.4% per week. How many years will it take for the stock to go from a value of $84 per share to a value of $1?

A) 2 years
B) 3 years
C) 4 years
D) 5 years

Answer 1

It will take approximately 0.60 years, which is equivalent to 8 months, for the stock to go from $84 per share to $1.

Step-by-step explanation:

To find how many years it will take for the stock to go from a value of $84 per share to a value of $1, we need to determine how many times the value will be decreased by 18.4%. We can set up the equation: 84 * (1 - 0.184)^n = 1, where n represents the number of weeks it will take. Rearranging the equation and solving for n, we get: (1 - 0.184)^n = 1/84. Taking the logarithm base 0.816 to both sides, we get: n = log(1/84) / log(0.816).

Using a calculator, we find: n ≈ 31.34. Since there are 52 weeks in a year, we can determine the number of years it will take by dividing n by 52: years ≈ 31.34 / 52 ≈ 0.60 years. Therefore, it will take approximately 0.60 years, which is equivalent to 8 months, for the stock to go from $84 per share to $1.