Amount at maturity $6,000. Discount rate 3 1/2%. 160 day note. What’s the bank discount and proceeds? Use ordinary interest method.

We are given the following information:
- **Amount at maturity (Face Value)** = \$6,000
- **Discount rate** = 3.5% (or 0.035 as a decimal)
- **Time period** = 160 days
- We are to use the **ordinary interest method** (where a year is taken as 360 days).

### Step 1: Bank Discount Formula
The bank discount can be calculated using the formula:
\[
\text{Bank Discount} = \text{Face Value} \times \text{Discount Rate} \times \frac{\text{Time}}{360}
\]

Plugging in the given values:
\[
\text{Bank Discount} = 6000 \times 0.035 \times \frac{160}{360}
\]

\[
\text{Bank Discount} = 6000 \times 0.035 \times 0.4444
\]

\[
\text{Bank Discount} = 6000 \times 0.0155556
\]

\[
\text{Bank Discount} = 93.33
\]

Thus, the **bank discount** is \$93.33.

### Step 2: Calculate the Proceeds
The proceeds represent the amount the borrower will receive from the bank after the discount is applied. It is the difference between the face value and the bank discount.

\[
\text{Proceeds} = \text{Face Value} - \text{Bank Discount}
\]

\[
\text{Proceeds} = 6000 - 93.33
\]

\[
\text{Proceeds} = 5906.67
\]

Thus, the **proceeds** are \$5,906.67.

### Final Answers:
- **Bank Discount** = \$93.33
- **Proceeds** = \$5,906.67

Would you like further details or have any questions? Here are 5 related questions for you:

1. How would the calculation change if the discount rate were higher, say 5%?
2. What is the difference between ordinary interest and exact interest methods?
3. How does the length of the note affect the bank discount?
4. What would happen to the proceeds if the note were for 90 days instead of 160 days?
5. Can you explain how the discount method differs from interest in advance?

**Tip:** When using the ordinary interest method, always remember to assume 360 days in a year for simplicity, unlike the exact interest method which uses 365 days.

Learn how to calculate the bank discount and proceeds for a $6,000 note with a 3.5% discount rate over 160 days using the ordinary interest method. This problem explains the step-by-step process of determining both the bank discount and the proceeds. Ideal for students in Grades 10-12.

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