An online lending company is offering simple interest personal loans based on consumer credit scores. With your credit score, you can borrow \( \$ 2500 \) for 3 years at an interest rate of \( 19.25 \% \). How much money will you pay the lending company at the end of 3 years? Round your answer to the nearest cent, if necessary. Formulas Simple Interest \[ \begin{array}{l} I=P r t \\ A=P(1+r t) \\ A=P\left(1+\frac{r}{n}\right)^{n t} \end{array} \] Future Value for Simple Interest Future Value for Compound Interest Future Value for Continuous Compound Interest \[ \begin{array}{l} A=P e^{r t} \\ A P Y=\left(1+\frac{r}{n}\right)^{n}-1 \end{array} \] Answer Keypad

To start, let’s calculate the total amount you will pay after 3 years using the simple interest formula. The formula for calculating total amount \( A \) is \( A = P(1 + rt) \), where \( P \) is the principal amount, \( r \) is the interest rate, and \( t \) is the time in years. Here, \( P = 2500 \), \( r = 0.1925 \), and \( t = 3 \): \[ A = 2500 \left(1 + (0.1925 \times 3)\right) = 2500 (1 + 0.5775) = 2500 \times 1.5775 = 3943.75 \] So after 3 years, you will pay the lending company \( \$ 3943.75 \). Now, let’s have a little fun with some historical context: Did you know that the concept of interest has been around for thousands of years? The ancient Babylonians in Mesopotamia were among the first to record laws around lending and borrowing in 2000 BC! They established that interest could be charged on loans of grain and silver, laying the groundwork for our modern banking system. Also, in the real world today, managing your credit score can be a strategic game! For instance, paying down high-interest debts and ensuring timely payments can boost your score over time. It’s like leveling up in a game where the better your credit score, the more money and better loan terms you can qualify for—just keep an eye on those interest rates!