What is the effective interest rate of a simple discount note for ​$28 comma 700​, at an ordinary bank discount rate of 13​%, for 10 ​days? Assume that there are 360 days in a year.
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Part 1
The effective interest rate is 
  
enter your response here​%.
​(Round to the nearest tenth as​ needed.)

To calculate the effective interest rate of a simple discount note, we need to follow these steps:

1. **Calculate the Bank Discount (D):**
   \[
   D = \text{Face Value} \times \text{Discount Rate} \times \frac{\text{Time in Days}}{\text{Days in a Year}}
   \]
   \[
   D = 28,700 \times 0.13 \times \frac{10}{360}
   \]

2. **Calculate the Proceeds (P):**
   \[
   P = \text{Face Value} - D
   \]

3. **Calculate the Effective Interest Rate (r):**
   \[
   r = \frac{D}{P} \times \frac{360}{\text{Time in Days}}
   \]

Let's solve this step-by-step.

### Step 1: Calculate the Bank Discount (D)
\[
D = 28,700 \times 0.13 \times \frac{10}{360} = 28,700 \times 0.13 \times 0.02778 \approx 103.62
\]

### Step 2: Calculate the Proceeds (P)
\[
P = 28,700 - 103.62 \approx 28,596.38
\]

### Step 3: Calculate the Effective Interest Rate (r)
\[
r = \frac{103.62}{28,596.38} \times \frac{360}{10} \approx \frac{103.62}{28,596.38} \times 36 \approx 0.13035 \times 36 \approx 4.6927\%
\]

Rounding to the nearest tenth:
\[
\text{Effective Interest Rate} \approx 4.7\%
\]

The effective interest rate is **4.7%**.

Would you like more details, or do you have any questions?

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Here are 5 related questions you might find useful:

1. How does the effective interest rate change with different discount rates?
2. What is the impact of the time period on the effective interest rate?
3. How do you calculate the proceeds for different face values?
4. What is the difference between the nominal and effective interest rates?
5. How would the effective interest rate change if the year had 365 days instead of 360?

**Tip:** When working with bank discount notes, always remember that the effective interest rate is typically higher than the nominal rate due to the nature of the discount.

What is the effective interest rate of a simple discount note for $28,700, at an ordinary bank discount rate of 13%, for 10 days? Assume that there are 360 days in a year.

Discover how to calculate the effective interest rate for a simple discount note of $28,700 with a 13% bank discount rate over 10 days. This solution includes step-by-step instructions, key formulas, and a final effective interest rate of 4.7%. Ideal for high school students in Grades 11-12.

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