Find the discount and the proceeds using the following data.
Face
Value
Discount
Rate
Time in
Days
​$4600
9​%
90


To find the discount and the proceeds, we need to use the formula for calculating the discount and the proceeds for a given face value, discount rate, and time in days.

### 1. Discount Calculation
The formula for the discount is:

\[
\text{Discount} = \text{Face Value} \times \text{Discount Rate} \times \frac{\text{Time in Days}}{360}
\]

Where:
- Face Value = $4600
- Discount Rate = 9% = 0.09
- Time in Days = 90

Let's calculate the discount:

\[
\text{Discount} = 4600 \times 0.09 \times \frac{90}{360}
\]

### 2. Proceeds Calculation
The proceeds are calculated as:

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

Let's calculate these values.### Results:

1. **Discount**: $103.50
2. **Proceeds**: $4496.50

These are the calculated discount and proceeds based on the provided data.

Would you like more details or have any questions? Here are some related questions:

1. How would the discount change if the discount rate increased to 12%?
2. What would be the proceeds if the face value was $5000 instead of $4600?
3. How would the discount be affected if the time in days was 180 days?
4. Can you calculate the proceeds if the face value, discount rate, and time in days all doubled?
5. How is the time factor important in calculating the discount?

**Tip**: Always ensure that the time in days is converted to a fraction of a year (usually using 360 or 365 days) when calculating discounts.

Find the discount and the proceeds using the following data. Face Value: $4600, Discount Rate: 9%, Time in Days: 90.

Learn how to calculate the discount and proceeds for a face value of $4600, a discount rate of 9%, and a time period of 90 days. This financial mathematics problem covers percentage-based calculations and is suitable for students in Grades 9-12.

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