An amount of \( \$ 33,000 \) is borrowed for 15 years at \( 8 \% \) interest, compounded annually. Assuming that no payments are made, find the amount owed after 15 years. Use the calculator provided and round your answer to the nearest dollar.

To find the amount owed after 15 years when borrowing \( \$ 33,000 \) at an 8% interest rate compounded annually, you can use the formula for compound interest: \[ A = P(1 + r)^n \] where: - \( A \) is the amount owed, - \( P \) is the principal amount (initial amount borrowed), - \( r \) is the annual interest rate (decimal), and - \( n \) is the number of years the money is borrowed. In this case: - \( P = 33,000 \) - \( r = 0.08 \) - \( n = 15 \) Substituting the values into the formula gives: \[ A = 33000(1 + 0.08)^{15} \] \[ A = 33000(1.08)^{15} \] \[ A = 33000(3.1728) \quad \text{(approximate value of \( (1.08)^{15} \))} \] \[ A \approx 104,202.40 \] Rounding to the nearest dollar, the amount owed after 15 years is approximately **\$104,202**. Now, here are some fun facts: While many people think of loans solely through the lens of immediate payments, the concept of compounding interest is a double-edged sword. It can work for you when saving, but against you when borrowing! This principle leads us to consider investments in various scenarios, such as how savings can grow exponentially over time with the right conditions. In practical situations, it’s essential to understand the impact of compound interest on loans. One common mistake borrowers make is not anticipating how seemingly manageable payments can balloon into substantial debts over time. By periodically reviewing the terms of your loans and interest accumulations, you can make more informed financial decisions, potentially saving yourself significant funds in the long run!