Josie has \( \$ 4,000 \) in an account that earns \( 5 \% \) interest compounded annually. To the nearest cent, how much interest will she earn in 1 year? Use the formula \( B=p(1+r)^{\prime} \), 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 years. \( \$ \) \( \square \) Sunmin

To find how much interest Josie will earn in 1 year, we first convert the interest rate from a percentage to a decimal: \( r = 0.05 \). Using the formula \( B = p(1 + r)^{t} \), where \( p = 4000 \), \( r = 0.05 \), and \( t = 1 \), we calculate \( B \): \[ B = 4000(1 + 0.05)^{1} = 4000(1.05) = 4200. \] Now, to find the interest earned, we subtract the principal from the balance: \( 4200 - 4000 = 200 \). So, Josie will earn \( \$200.00 \) in interest after 1 year. For a little historical context, the concept of compound interest dates back to ancient Mesopotamia, around 3000 BC! The Babylonians used it primarily in the context of agricultural loans, creating a system that would eventually evolve into what we recognize today. For those looking to apply this knowledge in real life, it's essential to understand how compound interest works for savings. By starting savings accounts early or investing in interest-bearing accounts, even modest contributions can grow significantly over time due to the snowball effect of compounding!