Final answer:
To calculate the balance of a savings account after 4 years with compound interest, the formula A = P(1 + r/n)^(nt) is used. Plugging in the provided values, the balance is approximately $866.57.
Step-by-step explanation:
To calculate the balance of the account after 4 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the balance after t years, P is the principal amount (initial deposit), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
In this case, P = $750, r = 5% = 0.05, n = 4 (quarterly compounding), and t = 4. Plugging in these values into the formula:
- A = 750(1 + 0.05/4)^(4*4)
- A = 750(1 + 0.0125)^16
- A = 750(1.0125)^16
- A ≈ $866.57
Therefore, the balance of the account after 4 years is approximately $866.57.