Edgar has \( \$ 7,000 \) in an account that earns \( 15 \% \) Interest compounded annually. To the nearest cent, how much interest will he earn in 3 years? Use the formula \( B=p(1+r)^{2} \), where \( B \) is the balance (final amount), \( p \) is the principal (starting amount), \( r \) is the interest rate expressed as a decimal, and \( t \) is the time in year

To find the amount of interest Edgar will earn in 3 years, we first need to substitute the values into the formula \( B = p(1+r)^{t} \). Here, \( p = 7000 \), \( r = 0.15 \), and \( t = 3 \). Calculating that, we have: \[ B = 7000(1 + 0.15)^{3} = 7000(1.15)^{3} \approx 7000(1.520875) \approx 10645.13 \] Now, subtract the principal from the final balance to get the interest earned: \[ \text{Interest} = B - p = 10645.13 - 7000 = 3645.13 \] Thus, to the nearest cent, Edgar will earn approximately \( \$3645.13 \) in interest over 3 years. But wait, let’s not skip over how interest rates can sometimes feel like magic! Did you know that historically, compounding interest dates back to ancient civilizations, with early mentions found in Babylonian records? It’s fascinating how a concept from thousands of years ago continues to impact our financial decisions today! Now, for some practical advice: when dealing with compounded interest, always pay attention to how frequently it's compounded—annually, semi-annually, or monthly—as it can significantly affect how much you earn over time. Missing out on that detail could make your financial projections less accurate!