1. A note has a maturity value of $10,000. If the term is 200 days and the simple discount rate is 9%, find (a) the amount of discount and (b) the proceeds.
2. To finance the building of a new fire station, the Farmview Fire District issued discount notes, each having a face value of $1,000 and a term of 5 years. The notes were sold at a simple notes, nt rate of 3%. Find the proceeds of each note sold.

Let's solve each question step by step:

### 1. A note has a maturity value of $10,000, a term of 200 days, and a simple discount rate of 9%. We need to find:
   - (a) the amount of the discount
   - (b) the proceeds

#### Formula for simple discount:
The simple discount formula is:

\[
\text{Discount} = M \times d \times \frac{t}{360}
\]

Where:
- $ M $ is the maturity value (future value) = $10,000
- $ d $ is the discount rate = 9% or 0.09
- $ t $ is the term in days = 200 days
- 360 is the banker's year, commonly used in finance

#### (a) The amount of the discount:
Substitute the given values:

\[
\text{Discount} = 10,000 \times 0.09 \times \frac{200}{360}
\]

Let’s calculate the discount.

\[
\text{Discount} = 10,000 \times 0.09 \times \frac{200}{360} = 500
\]

So, the amount of the discount is **$500**.

#### (b) The proceeds:
The proceeds are the amount the note is worth today, or the maturity value minus the discount:

\[
\text{Proceeds} = M - \text{Discount}
\]

Substitute the known values:

\[
\text{Proceeds} = 10,000 - 500 = 9,500
\]

So, the proceeds are **$9,500**.

---

### 2. The Farmview Fire District issued discount notes with a face value of $1,000, a term of 5 years, and a simple discount rate of 3%. We need to find the proceeds of each note sold.

#### Formula:
We will use the same simple discount formula:

\[
\text{Discount} = M \times d \times t
\]

Where:
- $ M $ is the face value (future value) = $1,000
- $ d $ is the discount rate = 3% or 0.03
- $ t $ is the term in years = 5

Substitute the known values:

\[
\text{Discount} = 1,000 \times 0.03 \times 5 = 150
\]

So, the discount is **$150**.

#### Proceeds:
The proceeds are the face value minus the discount:

\[
\text{Proceeds} = 1,000 - 150 = 850
\]

So, the proceeds are **$850** for each note sold.

---

### Summary:
1. **First note:**
   - (a) Discount = **$500**
   - (b) Proceeds = **$9,500**

2. **Second note:**
   - Proceeds = **$850**

---

Would you like more details or further explanations on any part?

Here are 5 related questions you might find helpful:
1. How is the simple interest rate different from the simple discount rate?
2. What would happen to the discount if the term were longer or shorter?
3. Can the simple discount formula be used for compounding interest situations?
4. How does the banker's year (360 days) affect the discount calculation?
5. What are the financial implications of issuing notes at a discount?

**Tip:** The "banker's year" of 360 days is often used for ease of calculation in financial contexts.

1. A note has a maturity value of $10,000. If the term is 200 days and the simple discount rate is 9%, find (a) the amount of discount and (b) the proceeds.
2. To finance the building of a new fire station, the Farmview Fire District issued discount notes, each having a face value of $1,000 and a term of 5 years. The notes were sold at a simple discount rate of 3%. Find the proceeds of each note sold.

Learn how to calculate the simple discount for a $10,000 note over 200 days with a 9% discount rate. Step-by-step instructions provided for finding both the discount amount and the proceeds. Includes an additional problem involving a $1,000 note at 3% over 5 years, making it suitable for Grades 10-12.

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