A student received an inheritance from her grandmother of \( \$ 3000 \). She places the money in a savings account paying simple interest at \( 5 \% \). What will be the value of the account after 6 months?

To find the value of the account after 6 months with simple interest, we can use the formula: \[ A = P(1 + rt) \] Where: - \( A \) is the total amount after time \( t \) - \( P \) is the principal amount (initial investment) - \( r \) is the rate of interest (expressed as a decimal) - \( t \) is the time in years For this situation: - \( P = 3000 \) - \( r = 0.05 \) - \( t = \frac{6}{12} = 0.5 \) years Now substituting the values into the formula: \[ A = 3000(1 + 0.05 \times 0.5) \] \[ A = 3000(1 + 0.025) \] \[ A = 3000(1.025) \] \[ A = 3075 \] So, the value of the account after 6 months will be \( \$ 3075 \). --- If you’re curious about simple interest in history, it has been used for thousands of years! Ancient Mesopotamia even used it as a way to encourage trade and agriculture, making it beneficial for both lenders and farmers. Imagine how different life would be without a simple way to grow your money over time! For real-world applications, consider how even a small amount of money, like that $3000, can work for you over time in savings accounts, investments, or bonds. Understanding how to leverage simple interest helps you make smart financial moves, whether for saving for college, a car, or even a fun vacation!