Final answer:
To calculate the time it takes to double your money if the interest is compounded continuously, use the formula A = Pe^(rt) and solve for t. In this case, it will take approximately 40.8 years to double your money.
Step-by-step explanation:
To calculate the time it takes to double your money if the interest is compounded continuously, we can use the formula A = Pe^(rt), where A is the final amount, P is the initial amount, e is the base of the natural logarithm, r is the interest rate, and t is the time in years. In this case, we are given that P = $3000, r = 1.7%, and we want to find t when A = 2P. Plugging in the values into the formula, we get 2P = P*e^(0.017t). Dividing both sides by P and taking the natural logarithm of both sides, we have ln(2) = 0.017t. Solving for t, t = ln(2)/0.017. Using a calculator, we find t ≈ 40.8 years. Therefore, it will take approximately 40.8 years to double your money if the interest is compounded continuously.