Face value $25,000. Rate of interest 9%. Date of note June 8. Date of note discounted July 10. Assume bank discount rate is 9%. What’s the maturity value, discount period, bank discount, proceeds?

Let's break this problem down step-by-step.

### Given Information:
- **Face value**: $25,000
- **Interest rate (rate of note)**: 9%
- **Date of note**: June 8
- **Date of note discounted**: July 10
- **Bank discount rate**: 9%

We'll assume a simple interest setup and apply the bank discount formula. Here's how to calculate each part:

---

### 1. **Maturity Value (MV)**:
The maturity value is the same as the face value of the note because it is the amount due at the end of the term. 

\[
\text{Maturity Value (MV)} = 25,000
\]

---

### 2. **Discount Period**:
The discount period is the time between the date the note was discounted (July 10) and the maturity date. Since the note was made on June 8, we need to determine the total time period, but we'll focus on the discount period from July 10 onward.

Since the term length is not provided, we'll assume it to be 90 days (a common assumption for notes), but you could adjust based on actual conditions.

From **July 10 to September 6** (the end of 90 days starting June 8), the discount period would be from July 10 to September 6. This is **58 days**.

---

### 3. **Bank Discount**:
The bank discount is calculated using the following formula:

\[
\text{Bank Discount} = \text{Face Value} \times \text{Bank Discount Rate} \times \left( \frac{\text{Discount Period}}{360} \right)
\]

Substituting the given values:

\[
\text{Bank Discount} = 25,000 \times 0.09 \times \left( \frac{58}{360} \right)
\]

\[
\text{Bank Discount} \approx 25,000 \times 0.09 \times 0.1611 = 362.48
\]

---

### 4. **Proceeds**:
The proceeds are the amount received after the bank deducts the discount from the face value of the note:

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

\[
\text{Proceeds} = 25,000 - 362.48 = 24,637.52
\]

---

### Final Answers:
- **Maturity Value (MV)**: $25,000
- **Discount Period**: 58 days
- **Bank Discount**: $362.48
- **Proceeds**: $24,637.52

---

Would you like further clarification or any details?

### Related questions:
1. How is the interest rate applied in a simple interest note?
2. What happens if the note term is different from 90 days?
3. How does the bank discount formula differ from the simple interest formula?
4. What is the impact of a higher or lower bank discount rate?
5. How does the discount period affect the proceeds of a note?

### Tip:
In problems involving bank discounts, always verify whether the 360-day year convention is used, as it's common for financial calculations.

Learn how to calculate the maturity value, discount period, bank discount, and proceeds for a $25,000 note with a 9% interest rate. This problem explores financial concepts including the simple interest formula and bank discount formula. Suitable for high school students in Grades 10-12.

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