\begin{tabular}{|l}\hline You decide to borrow \( \$ 26,000 \) to put in a new swimming pool. You obtain a loan for 30 \\ years, making equal monthly payments. After how many years will the greatest amount of \\ your payment be going toward interest? \\ \hline\( \square 25 \) years \\ \( \square 29 \) years \\ \( \square 5 \) years \\ \( \square 1 \) year \\ \hline\end{tabular}

We start by noting that for an amortized loan the monthly payment is fixed and is composed of an interest portion and a principal portion. In any given month the interest portion is calculated as \[ \text{Interest} = r \times \text{Outstanding Principal}, \] where \( r \) is the monthly interest rate. Because each payment reduces the outstanding principal, the interest portion in subsequent payments is smaller. Thus, immediately after the loan is taken (i.e. in the very first payments) the outstanding principal is at its maximum. Consequently, the interest part of the monthly payment is largest at the start and steadily decreases thereafter. Since the question asks “after how many years will the greatest amount of your payment be going toward interest?”, we recognize that the highest interest component occurs right at the beginning of the loan. Viewing the schedule in annual terms, the first year’s monthly payments include the highest interest portions. Therefore, the correct answer is \[ \boxed{1\text{ year}}. \]