Step 1 :Given values are: initial deposit \(A_{0} = \$10500\), annual interest rate \(r = 2.1\% = 0.021\), number of times interest is compounded per year \(n = 4\), and number of years \(t = 7\).
Step 2 :The account balance can be modeled by the compound interest formula \(A(t)=A_{0}\left(1+\frac{r}{n}\right)^{n t}\).
Step 3 :Substitute the given values into the formula: \(A = 10500 \times \left(1+\frac{0.021}{4}\right)^{4 \times 7}\).
Step 4 :Calculate the future value to find out how much money Juan will have in the account in 7 years.
Step 5 :The future value \(A\) is approximately \$12158.04.
Step 6 :For part (A), the values for \(A_{0}, r\), and \(n\) are: \(A_{0}=\boxed{10500}, r=\boxed{0.021}, n=\boxed{4}\).
Step 7 :For part (B), the amount of money Juan will have in the account in 7 years is: \(\boxed{\$12158.04}\).