Final answer:
To find the number of years it will take for the account balance to reach $7,989.80 with a fixed annual interest rate of 4% compounded continuously, we can use the formula for compound interest. Plugging in the values and solving for time, it will take approximately 5 years for the account balance to reach $7,989.80.
Step-by-step explanation:
To find the number of years it will take for the account balance to reach $7,989.80, we can use the formula for compound interest: A = P imes e^{rt}. In this formula, A is the final balance, P is the initial principal, r is the interest rate, and t is the time in years.
Plugging in the given values, we have: 7989.80 = 6285 imes e^{0.04t}. To solve for t, we need to isolate it by dividing both sides of the equation by 6285 and taking the natural logarithm of both sides. This gives us: t = ln(7989.80/6285) / 0.04.
Calculating this expression gives us t ≈ 5 years, so the correct answer is B) 5 years.