Answer:
it will take approximately 15.42 years for an investment of $567 at 4.5% continuous compounding to double to $1134.
Explanation:
The formula for continuously compounded interest is:
A = Pe^(rt)
where A is the final amount, P is the initial principal, r is the annual interest rate, t is the time in years, and e is the mathematical constant approximately equal to 2.71828.
We want to know how long it will take for an initial investment of $567 to double, so our final amount will be $1134. We know that the interest rate is 4.5% or 0.045 as a decimal. Substituting these values into the formula, we get:
1134 = 567e^(0.045t)
Dividing both sides by 567, we get:
2 = e^(0.045t)
Taking the natural logarithm of both sides, we get:
ln(2) = 0.045t
Solving for t, we get:
t = ln(2)/0.045
Using a calculator, we get:
t ≈ 15.42 years
Therefore, it will take approximately 15.42 years for an investment of $567 at 4.5% continuous compounding to double to $1134.