Face value $50,000. Rate of interest 11%. Length of note 95 days. Date of note June 10. Date of note discounted July 18. What’s the maturity value, discount period, bank discount, and proceeds?

Let's break this problem down step by step:

### Given:
- **Face Value** = $50,000
- **Rate of Interest (Annual)** = 11%
- **Length of Note** = 95 days
- **Date of Note** = June 10
- **Date Note Discounted** = July 18

### Step 1: Calculate the Maturity Date
The note has a length of **95 days** starting from June 10. We'll calculate the maturity date by adding 95 days to June 10.

- From **June 10** to **June 30**: 20 days
- Remaining days: $95 - 20 = 75$ days
- 75 days in **July**: 31 days in July
- Remaining days: $75 - 31 = 44$ days

Thus, the maturity date is **August 31 + 13 days = September 13**.

### Step 2: Calculate the Maturity Value
Since the note does not mention any compounding or other adjustments, the **Maturity Value** is equal to the face value:
\[
\text{Maturity Value} = \$50,000
\]

### Step 3: Determine the Discount Period
The note was issued on June 10 and discounted on July 18. The discount period is the time remaining until the note matures (from July 18 to September 13).

- From **July 18** to **July 31**: 13 days
- From **August 1** to **August 31**: 31 days
- From **September 1** to **September 13**: 13 days

Thus, the total **discount period** is:
\[
13 + 31 + 13 = 57 \text{ days}
\]

### Step 4: Calculate the Bank Discount
The bank discount is based on the face value of the note, the interest rate, and the discount period.

Using the **bank discount formula**:
\[
\text{Bank Discount} = \text{Face Value} \times \frac{\text{Rate} \times \text{Discount Period}}{360}
\]

Substitute the values:
\[
\text{Bank Discount} = 50,000 \times \frac{0.11 \times 57}{360} = 50,000 \times 0.0174167 = 870.83
\]

So, the **Bank Discount** is approximately:
\[
\$870.83
\]

### Step 5: Calculate the Proceeds
The proceeds are the amount received by the holder of the note after the discount is deducted from the face value. 

\[
\text{Proceeds} = \text{Face Value} - \text{Bank Discount}
\]
\[
\text{Proceeds} = 50,000 - 870.83 = 49,129.17
\]

Thus, the **Proceeds** amount to:
\[
\$49,129.17
\]

### Summary:
- **Maturity Value**: $50,000
- **Discount Period**: 57 days
- **Bank Discount**: $870.83
- **Proceeds**: $49,129.17

Would you like further details on any of these steps? 

Here are 5 related questions to deepen understanding:
1. How would the calculation change if the note was discounted on a different date?
2. What would happen if the interest rate were compounded monthly instead of simple interest?
3. How does the discount period affect the proceeds of the note?
4. How would the calculation differ if the discount period were 360 days instead of 365?
5. What if the note had a different face value, how would it impact each result?

**Tip:** Always use 360 days in financial calculations involving interest unless instructed otherwise, as it's standard in banking to simplify computations.

Learn how to calculate the maturity value, discount period, bank discount, and proceeds for a $50,000 note at 11% interest. This example covers key financial concepts including simple interest and discounting, suitable for students in Grades 10-12.

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