Darius has a 6-month loan for \( \$ 500 \). He must pay \( 5.6 \% \) annual interest on the loan. Using the formula for simple interest, \( I= \) Prt, where \( I \) is interest owed, \( P \) is the amount borrowed, \( r \) is the rate as a decimal, and \( t \) is time in years, find the amount of interest owed by Darius after 6 months. \( \$ 168 \) \( \$ 16.80 \) \$140 \( \$ 14 \)

To calculate the interest owed by Darius after 6 months, we can plug the values into the simple interest formula \( I = Prt \). Here, \( P = 500 \), \( r = 0.056 \) (which is 5.6% as a decimal), and \( t = 0.5 \) (since 6 months is half a year). So, \( I = 500 * 0.056 * 0.5 = 14 \). Therefore, Darius owes \( \$14 \) in interest. Finding out how such simple interest calculations can weave into our daily lives can be quite fun! Just think about when you’re shopping for a car, or even if you decide to take a small personal loan. Understanding the cost of what you're borrowing will help you make wiser financial decisions down the road. Imagine being able to compare offers based on just a few numbers! For those intrigued by how interest began, the concept dates back to ancient Mesopotamia! People were already borrowing and lending goods and money using a type of interest as early as 3000 BC. It was a way to encourage lending and manage economic trade. Fast forward to today, and it's a fundamental part of banking and finance, influencing everything from how we invest to the rates we pay on mortgages.