To find the balance after 8 years with continuous compounding, we can use the formula A = Pe^(rt), where:
A represents the final amount,
P is the initial principal (deposit),
e is the base of the natural logarithm (approximately 2.71828),
r is the interest rate (as a decimal), and
t is the time in years.
In this case, P = $1300, r = 3% = 0.03, and t = 8 years. Plugging these values into the formula, we have:
A = 1300 * e^(0.03 * 8)
Using a calculator, we can evaluate this expression:
A ≈ 1300 * e^(0.24) ≈ 1300 * 1.271249 ≈ $1654.62
Therefore, the balance after 8 years, with continuous compounding, would be approximately $1654.62.
