The correct answer is option A : $9482.20. The balance of Rose's account after all the interest is paid for the year on a principle balance will be $9482.20.
To calculate the balance of Rose's savings account after one year, we can use the formula for compound interest: A = P(1 + r/n)^(nt).
Where:
- A is the final amount in the account
- P is the principal balance
- r is the annual interest rate
- n is the number of times the interest is compounded per year
- t is the number of years
Plugging in the values for Rose's account : P = $9100, r = 4.2/100 = 0.042, n = 12 (compounded monthly), and t = 1 year :
A = $9100(1 + 0.042/12)^(12 * 1)
A ≈ $9482.20
Therefore, the balance of Rose's account after all the interest is paid for the year will be $9482.20.