What is the effective interest rate of a simple discount note for $31,200, at an ordinary bank discount rate of 14%, for 30 days? Assume that there are 360 days in a ye- The effective interest rate is %. (Round to the nearest tenth as needed.) CITE L
What is the effective interest rate of a simple discount note for $31,200, at an ordinary bank discount rate of 14%, for 30 days? Assume that there are 360 days in a ye- The effective interest rate is %. (Round to the nearest tenth as needed.) CITE L
Chapter1: Financial Statements And Business Decisions
Section: Chapter Questions
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![**Understanding Effective Interest Rates for Simple Discount Notes**
This section will help you understand how to calculate the effective interest rate of a simple discount note. Let's look at a specific example.
**Problem Statement:**
What is the effective interest rate of a simple discount note for $31,200, at an ordinary bank discount rate of 14%, for 30 days? Assume that there are 360 days in a year.
---
**Solution:**
1. **Calculate the Bank Discount:**
The bank discount is calculated using the formula:
\[
\text{Bank Discount} = \text{Face Value} \times \text{Discount Rate} \times \frac{\text{Time}}{360}
\]
Given:
- Face Value (FV) = $31,200
- Discount Rate (DR) = 14% = 0.14
- Time (T) = 30 days
\[
\text{Bank Discount} = 31,200 \times 0.14 \times \frac{30}{360} = 31,200 \times 0.14 \times 0.0833 = \$364.32
\]
2. **Determine the Proceeds (P):**
The proceeds are calculated as the face value minus the bank discount.
\[
\text{Proceeds} = \text{Face Value} - \text{Bank Discount} = 31,200 - 364.32 = \$30,835.68
\]
3. **Calculate the Effective Interest Rate (EIR):**
The effective interest rate on the proceeds can be found using the simple interest formula:
\[
\text{Effective Interest Rate} = \frac{\text{Interest (Bank Discount)}}{\text{Proceeds}} \times \frac{360}{\text{Time}}
\]
Substituting the given values:
\[
\text{Effective Interest Rate} = \frac{364.32}{30,835.68} \times \frac{360}{30} = \frac{364.32}{30,835.68} \times 12 = 0.141992 \approx 14.2\%
\]
Hence, the effective interest rate is approximately **14.2%**.
---
Feel free to use this example as a guide](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff3aaa20b-aa03-431c-a209-6c3af75044ad%2F9529d16e-c6e3-42b1-9c15-1d0c0373da34%2Ffxzmp1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Effective Interest Rates for Simple Discount Notes**
This section will help you understand how to calculate the effective interest rate of a simple discount note. Let's look at a specific example.
**Problem Statement:**
What is the effective interest rate of a simple discount note for $31,200, at an ordinary bank discount rate of 14%, for 30 days? Assume that there are 360 days in a year.
---
**Solution:**
1. **Calculate the Bank Discount:**
The bank discount is calculated using the formula:
\[
\text{Bank Discount} = \text{Face Value} \times \text{Discount Rate} \times \frac{\text{Time}}{360}
\]
Given:
- Face Value (FV) = $31,200
- Discount Rate (DR) = 14% = 0.14
- Time (T) = 30 days
\[
\text{Bank Discount} = 31,200 \times 0.14 \times \frac{30}{360} = 31,200 \times 0.14 \times 0.0833 = \$364.32
\]
2. **Determine the Proceeds (P):**
The proceeds are calculated as the face value minus the bank discount.
\[
\text{Proceeds} = \text{Face Value} - \text{Bank Discount} = 31,200 - 364.32 = \$30,835.68
\]
3. **Calculate the Effective Interest Rate (EIR):**
The effective interest rate on the proceeds can be found using the simple interest formula:
\[
\text{Effective Interest Rate} = \frac{\text{Interest (Bank Discount)}}{\text{Proceeds}} \times \frac{360}{\text{Time}}
\]
Substituting the given values:
\[
\text{Effective Interest Rate} = \frac{364.32}{30,835.68} \times \frac{360}{30} = \frac{364.32}{30,835.68} \times 12 = 0.141992 \approx 14.2\%
\]
Hence, the effective interest rate is approximately **14.2%**.
---
Feel free to use this example as a guide
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