Some investments in the stock market have earned 12% annually. At this rate, earnings can be found using the formula A = P(1.12)^n, where A is the total value of the investment, P is the initial value of the investment, and n is the number of years the money is invested. If $5000 is invested in the stock market at this annual rate of return, what is the expected total value after 20 years?
A = 5000 (1.12)^20
= 5000 * 9.646293
= 48,231.47
To find the expected total value after 20 years, we can use the formula A = P(1.12)^n, where A is the total value of the investment, P is the initial value of the investment, and n is the number of years the money is invested.
In this case, the initial value of the investment (P) is $5000, and the number of years (n) is 20. The annual rate of return is 12%, which can be expressed as 1.12 in decimal form.
Using the formula, we can substitute the values:
A = 5000(1.12)^20
To solve this, we calculate 1.12 raised to the power of 20 and then multiply it by $5000.
Now, let's calculate the value of 1.12 raised to the power of 20:
1.12^20 ≈ 6.191736422.
Next, we multiply this value by $5000 to find the expected total value after 20 years:
A ≈ 6.191736422 * 5000 ≈ $30958.68.
Therefore, the expected total value of the investment after 20 years is approximately $30958.68.