Use a banker's year described above to answer this question. To complete the sale of a house, the you accept a 300-day note for $5,000 at 6% simple interest. (Both interest and principal are repaid at the end of the 300 days.) Wishing to use the money sooner for the purchase of another house, the you sell the note to a third party for $5,177 after 40 days. What annual simple interest rate will the third party receive for the investment? Express your answer as a percentage. %. Round to the nearest thousandths of a percent (3 decimal places).
Use a banker's year described above to answer this question. To complete the sale of a house, the you accept a 300-day note for $5,000 at 6% simple interest. (Both interest and principal are repaid at the end of the 300 days.) Wishing to use the money sooner for the purchase of another house, the you sell the note to a third party for $5,177 after 40 days. What annual simple interest rate will the third party receive for the investment? Express your answer as a percentage. %. Round to the nearest thousandths of a percent (3 decimal places).
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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![**How to Determine the Annual Simple Interest Rate from a 300-Day Note**
**Scenario:**
To complete the sale of a house, you accept a 300-day note for $5,000 at 6% simple interest. (Both interest and principal are repaid at the end of the 300 days.) Wishing to use the money sooner for the purchase of another house, you sell the note to a third party for $5,177 after 40 days. What annual simple interest rate will the third party receive for the investment? Express your answer as a percentage.
**Guide to Solving the Problem:**
1. **Calculate the Interest on the Note:**
- Principal (P) = $5,000
- Annual Interest Rate (R) = 6%
- Time period (T) = 300 days
The formula for simple interest is:
\[
\text{Interest} = \frac{P \cdot R \cdot T}{365 \text{ days}}
\]
2. **Determine the Sale Price to the Third Party:**
- Sale Price = $5,177
- Number of Days Passed = 40 days
3. **Calculate the Remaining Time for the Third Party:**
- Remaining Time = 300 days - 40 days = 260 days
4. **Calculate the Total Amount to be Paid by the Third Party at the End of the Note's Term:**
The amount due (A) at the end of the period:
\[
A = P + \text{Interest}
\]
5. **Determine the Annual Simple Interest Rate for the Third Party:**
Use the formula to find the annual simple interest rate offered to the third party:
\[
R_{\text{third party}} = \frac{(\text{Future Value} - \text{Present Value}) \cdot 365}{\text{Present Value} \cdot \text{Remaining Time}}
\]
6. **Final Calculation:**
Round the result to the nearest thousandth of a percent (3 decimal places).
**Solution Start:** [Enter your detailed solution here]
___________%
Round to the nearest thousandths of a percent (3 decimal places).
By understanding and following these steps, you can determine the annual simple interest rate received by the third party for their investment in this note.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d929fa4-2fdc-40c7-801d-1fbf9b4298bd%2F6073ce00-c6f9-4410-912d-3c625e95c4a4%2F86vt5ip_processed.png&w=3840&q=75)
Transcribed Image Text:**How to Determine the Annual Simple Interest Rate from a 300-Day Note**
**Scenario:**
To complete the sale of a house, you accept a 300-day note for $5,000 at 6% simple interest. (Both interest and principal are repaid at the end of the 300 days.) Wishing to use the money sooner for the purchase of another house, you sell the note to a third party for $5,177 after 40 days. What annual simple interest rate will the third party receive for the investment? Express your answer as a percentage.
**Guide to Solving the Problem:**
1. **Calculate the Interest on the Note:**
- Principal (P) = $5,000
- Annual Interest Rate (R) = 6%
- Time period (T) = 300 days
The formula for simple interest is:
\[
\text{Interest} = \frac{P \cdot R \cdot T}{365 \text{ days}}
\]
2. **Determine the Sale Price to the Third Party:**
- Sale Price = $5,177
- Number of Days Passed = 40 days
3. **Calculate the Remaining Time for the Third Party:**
- Remaining Time = 300 days - 40 days = 260 days
4. **Calculate the Total Amount to be Paid by the Third Party at the End of the Note's Term:**
The amount due (A) at the end of the period:
\[
A = P + \text{Interest}
\]
5. **Determine the Annual Simple Interest Rate for the Third Party:**
Use the formula to find the annual simple interest rate offered to the third party:
\[
R_{\text{third party}} = \frac{(\text{Future Value} - \text{Present Value}) \cdot 365}{\text{Present Value} \cdot \text{Remaining Time}}
\]
6. **Final Calculation:**
Round the result to the nearest thousandth of a percent (3 decimal places).
**Solution Start:** [Enter your detailed solution here]
___________%
Round to the nearest thousandths of a percent (3 decimal places).
By understanding and following these steps, you can determine the annual simple interest rate received by the third party for their investment in this note.
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