Final answer:
To find the value of a stock that depreciates by 9.5% each year over 4 years from an initial value of $100, we use the compound decay formula: A = 100(1 - 0.095)^4, which gives us an approximate value of $66.73.
Step-by-step explanation:
The question asks for the value of a stock that decreases by 9.5% each year over a period of four years from an initial value of $100. This is a mathematics problem where the concept of compound interest is applied in reverse, known as decay when dealing with a decrease in value over time.
To calculate the value after each year, we can use the formula for compound decay, which is A = P(1 - r)^n, where A is the amount after n years, P is the initial principal balance, r is the rate of decrease, and n is the number of times the interest is applied (number of years).
Using the formula:
-
- P = $100 (the initial value of the stock)
-
- r = 0.095 (which represents the 9.5% decrease written as a decimal)
-
- n = 4 (since we are looking at four years into the future)
We calculate the value of the stock after 4 years as follows:
A = 100(1 - 0.095)^4
A = 100(0.905)^4
A ≈ $100 * 0.6673
A ≈ $66.73
The value of the stock after 4 years would be approximately $66.73.