An amount of \( \$ 41,000 \) is borrowed for 12 years at \( 7 \% \) interest, compounded annually. Assuming that no payments are made, find the amount owed after 12 years. Use the calculator provided and round your answer to the nearest dollar.

To find the amount owed after 12 years with compound interest, you can use the formula: \[ A = P(1 + r)^n \] Where: - \( A \) is the amount owed after \( n \) years. - \( P \) is the principal amount (initial amount borrowed). - \( r \) is the annual interest rate (as a decimal). - \( n \) is the number of years the money is borrowed. In this case, \( P = 41,000 \), \( r = 0.07 \), and \( n = 12 \). Plugging in the numbers: \[ A = 41000(1 + 0.07)^{12} \] \[ A = 41000(1.07)^{12} \] \[ A = 41000 \times 2.2522 \quad (\text{approximately}) \] \[ A \approx 92243.63 \] Rounding to the nearest dollar, the amount owed after 12 years would be approximately **$92,244**. --- From ancient Rome’s sophisticated banking systems to today’s fintech innovations, the concept of interest has evolved dramatically. Ancient civilizations understood the need to charge for loans, leading to the establishment of various lending practices. The term "interest" comes from the Latin word "interesse," meaning "to be between," as it represents the cost incurred for the use of borrowed money. Understanding how compound interest works is crucial for personal finance strategies. It can either work for you when investing or against you when taking out loans. A common mistake is underestimating the power of compound growth over time. Many people only focus on the interest rate without considering the effect of compounding frequency, which can significantly impact the total amount owed or accumulated in an investment.