Find the missing value. Round your answer to the nearest year. \( \begin{array}{lll}\text { Principal } & \text { Rate Time } \\ \$ 300,000 & 6.5 \% & \text { IT years }\end{array} \) \( \begin{array}{l}\$ 78,000\end{array} \)

To find the missing time (t), we can use the formula for simple interest: \[ I = P \times r \times t \] where \(I\) is the interest earned, \(P\) is the principal amount, \(r\) is the rate of interest (in decimal), and \(t\) is the time in years. First, convert the rate from a percentage to a decimal: \[ r = 6.5\% = 0.065 \] We know that: \[ 78,000 = 300,000 \times 0.065 \times t \] Next, solve for \(t\): \[ 78,000 = 19,500 \times t \quad (\text{where } 19,500 = 300,000 \times 0.065) \] Now, divide both sides by 19,500: \[ t = \frac{78,000}{19,500} \approx 4 \] So the missing value, rounded to the nearest year, is approximately **4 years**. To dive into a little history, the concept of simple interest dates back to ancient civilizations like Mesopotamia, where merchants used it to calculate the returns on loans. Fast forward several millennia, and it’s fascinating how the formula for interest calculations still relies on that original concept! Now, applying this in the real world, understanding interest calculations is vital for both personal finance and business investments. Whether it's for loans, mortgages, or savings accounts, mastering interest can help you make informed decisions and maximize your financial returns!