Final answer:
To determine how long it would take for the value of the account to reach $360 with an interest rate of 2.1% compounded continuously, we can use the formula for compound interest and solve for time. Using the given values, it would take approximately 7.9 years for the value of the account to reach $360.
Step-by-step explanation:
To determine how long it would take for the value of the account to reach $360, we can use the formula for compound interest: A = P * e^(rt), where A is the final amount, P is the initial amount, e is the base of natural logarithms, r is the interest rate, and t is the time in years. In this case, we know that P = $280, A = $360, and r = 0.021. Using these values, we can solve for t:
360 = 280 * e^(0.021t)
Dividing both sides by 280:
1.2857 = e^(0.021t)
Taking the natural logarithm of both sides:
ln(1.2857) = 0.021t
Dividing both sides by 0.021:
t = ln(1.2857) / 0.021
Using a calculator, we find that t ≈ 7.91. Therefore, it would take approximately 7.9 years for the value of the account to reach $360.