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Part 1
What is the effective interest rate of a simple discount note for ​$28 comma 500​, at an ordinary bank discount rate of 14​%, for 20 ​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 find the effective interest rate of a simple discount note, we first need to understand the steps involved:

### Step 1: Calculate the Discount Amount
The formula to calculate the discount amount ($ D $) is:
\[
D = \text{Face Value} \times \text{Bank Discount Rate} \times \frac{\text{Time}}{\text{Number of Days in a Year}}
\]

Where:
- Face Value = \$28,500
- Bank Discount Rate = 14% or 0.14
- Time = 20 days
- Number of Days in a Year = 360

\[
D = 28,500 \times 0.14 \times \frac{20}{360}
\]

### Step 2: Calculate the Proceeds
The proceeds ($ P $) is the amount that the borrower actually receives, which is the face value minus the discount:
\[
P = \text{Face Value} - D
\]

### Step 3: Calculate the Effective Interest Rate
The effective interest rate ($ r_{\text{eff}} $) is calculated using the formula:
\[
r_{\text{eff}} = \frac{D}{P} \times \frac{360}{\text{Time}} \times 100
\]

Let's compute the values.

#### Step 1: Calculate the Discount
\[
D = 28,500 \times 0.14 \times \frac{20}{360} \approx 221.67
\]

#### Step 2: Calculate the Proceeds
\[
P = 28,500 - 221.67 \approx 28,278.33
\]

#### Step 3: Calculate the Effective Interest Rate
\[
r_{\text{eff}} = \frac{221.67}{28,278.33} \times \frac{360}{20} \times 100 \approx 14.1\%
\]

### Final Answer
The effective interest rate is approximately **14.1%**.

Would you like any additional details or have further questions?

Here are 5 related questions to deepen your understanding:
1. How does the effective interest rate change if the discount period is extended to 30 days?
2. What would the effective interest rate be if the bank discount rate was 12% instead of 14%?
3. How would the effective interest rate differ if the note had a face value of $50,000?
4. Can you explain the difference between the nominal interest rate and the effective interest rate?
5. How is the effective interest rate affected by the number of days in a year (360 vs. 365)?

**Tip:** The effective interest rate will always be higher than the nominal discount rate because it takes into account the actual proceeds received by the borrower, which are lower than the face value of the note.

What is the effective interest rate of a simple discount note for $28,500, at an ordinary bank discount rate of 14%, for 20 days? Assume that there are 360 days in a year.

Discover how to calculate the effective interest rate of a simple discount note with a face value of $28,500, a bank discount rate of 14%, and a 20-day term. Learn step-by-step calculations, including determining the discount amount, proceeds, and effective interest rate. Perfect for high school students in Grades 11-12.

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