The correct answer is B. 36 years.
Step-by-step explanation:
Let's use the continuous compounding formula to solve the problem:
A = Pe^(rt)
A is the final amount, P is the initial amount, e is the mathematical constant equal to approximately 2.71828, r is the annual interest rate, and t is the time in years.
We want to find the time it takes for the initial amount P to triple, which means that A = 3P. Substituting this into the formula, we get:
3P = Pe^(rt)
Dividing both sides by P, we get:
3 = e^(rt)
Taking the natural logarithm of both sides, we get:
ln(3) = rt
Solving for t, we get:
t = ln(3)/r
Substituting the values of P, r, and e, we get:
t = ln(3)/(0.03)
t ≈ 36.6 years
So, it will take approximately 36 years for the initial amount of $1000 to triple at an annual interest rate of 3% with continuous compounding. The closest answer choice is B. 36 years.