Final answer:
The balance in the account after 30 years will be approximately $8884.68. The interest earned for the entire time period is approximately $4284.68.
Step-by-step explanation:
To find the balance of an account with quarterly compounding, we can use the compound interest formula: A = P(1 + r/n)^(nt). Where A is the balance, P is the initial deposit, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, P = $4600, r = 0.018 (1.8% expressed as a decimal), n = 4 (quarterly compounding), and t = 30. Plugging in these values, we get: A = $4600(1 + 0.018/4)^(4*30) = $4600(1.0045)^(120) ≈ $8884.68. Therefore, the balance in the account after 30 years will be approximately $8884.68.
To find the interest earned, we subtract the initial deposit from the final balance: Interest = A - P = $8884.68 - $4600 = $4284.68. Therefore, the interest earned for the entire time period is approximately $4284.68.