Final answer:
To find the balance after one year with an annual interest rate of 19% on a $25,000 loan, compound interest is applied, resulting in a new balance of $29,750.
Step-by-step explanation:
The question is asking about the future balance of a loan with a given initial balance and annual compounding interest rate. To calculate the balance after one year, you use the formula for compound interest, which is A = P(1 + r/n)^(nt). Here, P is the principal amount ($25,000), r is the annual interest rate (0.19), n is the number of times that interest is compounded per year (1 for annually), and t is the time the money is invested or borrowed for, in years (1 year). Therefore, the formula becomes A = $25,000(1 + 0.19/1)^(1*1), which simplifies to A = $25,000(1 + 0.19), and finally A = $25,000 * 1.19 = $29,750. So the correct answer is A) $29,750.