Final answer:
To find how long it takes for an investment to double in value at 8% compounded continuously, we can use the formula for continuous compound interest.
Step-by-step explanation:
To find out how long it takes for an investment to double in value if it is invested at 8% compounded continuously, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
- A is the final amount
- P is the initial investment
- e is Euler's number (approximately 2.71828)
- r is the interest rate (in decimal form)
- t is the time (in years)
We want to find the value of t when the final amount (A) is double the initial investment (P). So, we have:
2P = P * e^(0.08t)
To simplify, we can divide both sides by P:
2 = e^(0.08t)
Now, we can take the natural logarithm of both sides to solve for t:
ln(2) = 0.08t
Finally, divide both sides by 0.08 to isolate t:
t ≈ ln(2) / 0.08
Using a calculator, the approximate value of t is about 8.66 years. Therefore, the answer is a. ≈8.66 years.