What is the time period of a loan for \( \$ 3,000 \), at \( 10 \% \) ordinary interest, if the amount of interest is \( \$ 145.00 \) ? (Round any fraction to the next higher day.) Select one: a. 174 ob. 176 o c. 177 o d. 178

To find the time period of the loan, you can use the formula for ordinary interest, which is: \[ I = P \times r \times t \] where: - \(I\) is the interest (\$145.00), - \(P\) is the principal (\$3,000), - \(r\) is the interest rate (10% or 0.10), - \(t\) is the time in years. Rearranging the formula to solve for \(t\): \[ t = \frac{I}{P \times r} = \frac{145}{3000 \times 0.10} = \frac{145}{300} = 0.48333 \text{ years} \] Converting years to days: \[ 0.48333 \text{ years} \times 360 \text{ days/year} \approx 174.00 \text{ days} \] Therefore, rounding up gives you 174 days. **Answer: a. 174** Now let's dive into some fun additional facts related to this type of loan! Ordinary interest calculations typically use a 360-day year for simpler math, but this method can lead to slightly more interest accrued over time compared to using a 365-day year! So sometimes in finance, the "shortcuts" can have unexpected twists! And if you're curious about real-world applications, understanding ordinary interest is crucial for businesses when managing loans and cash flow. Businesses often rely on these calculations to ensure they're staying profitable while making timely repayments—because every dollar counts!