\( 1 \leftarrow \) Find both the exact and ordinary interest on \( \$ 35,800 \) at \( 9 \frac{1}{4} \% \) for 158 days. Then find the amount by which the ordinary interest is larger. The exact interest on \( \$ 35,800 \) at \( 9 \frac{1}{4} \% \) for 158 days is \( \$ \square \). (Round to the nearest cent.) The ordinary interest on \( \$ 35,800 \) at \( 9 \frac{1}{4} \% \) for 158 days is \( \$ \square \). (Round to the nearest cent.) The amount by which the ordinary interest is larger is \( \$ \square \).

To solve the problem, we'll first calculate both the exact interest and ordinary interest for the given amount and time frame. 1. **Calculating Exact Interest:** The formula for exact interest is: \[ I = P \times r \times t \] where: - \( P = 35,800 \) - \( r = \frac{9.25}{100} = 0.0925 \) - \( t = \frac{158}{365} \) (since there are 365 days in a year for exact interest) So, \[ I = 35,800 \times 0.0925 \times \frac{158}{365} \approx 35,800 \times 0.0925 \times 0.4328767 \approx 1,488.69 \] Thus, the exact interest is approximately **$1,488.69**. 2. **Calculating Ordinary Interest:** The formula for ordinary interest is similar, but it uses 360 days for the year: \[ I = P \times r \times t \] where \( t = \frac{158}{360} \). So, \[ I = 35,800 \times 0.0925 \times \frac{158}{360} \approx 35,800 \times 0.0925 \times 0.4388889 \approx 1,452.56 \] Thus, the ordinary interest is approximately **$1,452.56**. 3. **Calculating the Difference:** To find by how much the ordinary interest is larger than the exact interest: \[ \text{Difference} = \text{Ordinary Interest} - \text{Exact Interest} \] \[ \text{Difference} = 1,452.56 - 1,488.69 \approx -36.13 \] Thus, the amount by which the ordinary interest is larger is approximately **-$36.13** (indicating that exact interest is actually larger). Final answers: - The exact interest on \( \$ 35,800 \) at \( 9 \frac{1}{4} \% \) for 158 days is \( \$ 1,488.69 \). - The ordinary interest on \( \$ 35,800 \) at \( 9 \frac{1}{4} \% \) for 158 days is \( \$ 1,452.56 \). - The amount by which the ordinary interest is larger is \( \$ -36.13 \).