Determine " \( n \) " if an amount is invested for 3.5 years at \( 2.25 \% \) compound quarterly.

To find out the total amount \( A \) after investing for \( n \) years at \( r \) percent interest compounded quarterly, we use the formula: \[ A = P \left(1 + \frac{r}{m}\right)^{mt} \] where: - \( P \) is the principal amount (initial investment), - \( r \) is the annual interest rate (in decimal form), - \( m \) is the number of times interest is compounded per year, - \( t \) is the number of years. For \( n = 3.5 \) years, the interest rate \( r = 2.25\% = 0.0225 \) (as a decimal), and since it’s compounded quarterly, \( m = 4 \). Now, plug in these values into the formula to calculate \( A \) given \( P \), or if looking for time, set \( A = f(P) \) as per your goal. For now, you'll have: \[ A = P \left(1 + \frac{0.0225}{4}\right)^{4 \times 3.5} \] For a practical example, let’s say \( P = 1000 \): \[ A = 1000 \left(1 + 0.005625\right)^{14} \approx 1000 (1.005625)^{14} \] Evaluate to find \( A \), or use numerical or computational tools for an exact decimal output. Happy calculating!