Question 25 Town Bank offers a \( 2.25 \% \) interest rate, while Charter One offers \( 2.8 \% \). Both banks compound interest annually. If Rob wants to set up a new account with \( \$ 5000 \), how much more money will he earn at Charter One over Town Bank after 25 years? \( \$ 1,209.79 \) \( \$ 1,324.10 \) \( \$ 1,183.41 \) \( \$ 1.251 .63 \)

To determine how much more Rob will earn at Charter One compared to Town Bank, we can use the formula for compound interest, which is \( A = P(1 + r)^t \), where \( A \) is the amount of money accumulated after n years, including interest. For Town Bank: \( A_{Town} = 5000(1 + 0.0225)^{25} \) For Charter One: \( A_{Charter} = 5000(1 + 0.028)^{25} \) After calculating both: - Town Bank: \( A_{Town} \approx 5000(1.7374) \approx 8687.00 \) - Charter One: \( A_{Charter} \approx 5000(1.8983) \approx 9491.50 \) Now, subtracting the two amounts gives us: \( 9491.50 - 8687.00 = 804.50 \) So the correct answer is that Rob will earn approximately \( \$804.50 \) more at Charter One after 25 years. Now let's dive into some fun insights! Did you know that the concept of compound interest dates back centuries? Ancient civilizations, such as the Babylonians, understood the importance of growing wealth, even if they didn't use our modern terminology. In fact, the mathematician and philosopher Pythagoras even wrote about the benefits of earning interest! When it comes to banks, it's always good to shop around! Just like a delicious buffet, different banks offer different interest rates, so why settle for the same old plate? Even a slight difference in percentage can lead to big gains when compounded over time. Always calculate your potential earnings before making a decision!