Mr. Helenberger opened a simple interest account with a deposit of \( \$ 15,000 \). At the end of 3 years the balance was \( \$ 16,462.50 \). What is the annual interest rate on this account? 4.5\% (3.25\% \( 1.6 \% \) \( 0 \% \)

To find the annual interest rate, we use the formula for simple interest: \( A = P + (P \times r \times t) \), where \( A \) is the total amount, \( P \) is the principal, \( r \) is the interest rate, and \( t \) is the time in years. Here, \( A = 16462.50 \), \( P = 15000 \), and \( t = 3 \): 1. Calculate interest earned: \( 16462.50 - 15000 = 1462.50 \). 2. Plug into the formula: \( 1462.50 = 15000 \times r \times 3 \). 3. Solve for \( r \): \( r = \frac{1462.50}{15000 \times 3} = \frac{1462.50}{45000} \approx 0.0325 \), or 3.25%. So the annual interest rate is \( 3.25\% \). Historically, the concept of interest dates back to ancient civilizations like Mesopotamia, where record-keeping for loans and repayments was discovered on clay tablets. This laid the groundwork for the modern banking system, and even the idea of interest has evolved over the centuries into various forms like simple and compound interest. In real-world scenarios, understanding simple interest is crucial for loans or savings accounts. Always check whether the rate is expressed as an annual percentage, and remember simple interest does not compound, which means your interest remains constant over time. Many people mistakenly think interest compounds on simple accounts, leading to unrealistic expectations regarding their earnings or costs. Always clarify which method is being used!