Use the compound interest formula to compute the balance in the following account after the stated period of time, assuming interest is compounded annually. \( \$ 12,000 \) invested at an APR of \( 2.3 \% \) for 13 years. The balance in the account after 13 years is \( \$ \square \). (Round to the nearest cent as needed.)

To find the balance using the compound interest formula \( A = P(1 + r)^t \), where \( A \) is the amount of money accumulated after n years, including interest, \( P \) is the principal amount (the initial amount of money), \( r \) is the annual interest rate (decimal), and \( t \) is the number of years the money is invested or borrowed. Here, \( P = 12,000 \), \( r = 0.023 \) (which is 2.3% expressed as a decimal), and \( t = 13 \). Now plug in the values: \[ A = 12000(1 + 0.023)^{13} \] \[ A = 12000(1.023)^{13} \] \[ A \approx 12000 \times 1.34547 \, [\text{calculating } (1.023)^{13}] \] \[ A \approx 16145.64 \] Therefore, the balance in the account after 13 years is approximately \( \$ 16,145.64 \).