After 5 years, with a principal of $3000 and an annual interest rate of 3.5% compounded continuously, the account will have approximately $3606.78.
To calculate the amount in the account after 5 years with continuous compounding, you can use the formula for compound interest: A = Pe^(rt), where:
- Plugging the values into the formula gives:
A = 3000 * e^(0.035*5) = 3000 * e^0.175 = 3000 * 2.71828^0.175 ≈ $3000 * 1.20226 ≈ $3606.78
After 5 years, the account will have approximately $3606.78 when the interest is compounded continuously.