What annual interest rate is earned by a 17-week T-bill with a maturity value of $1,700 that sells for $1,680.88? ... The annual interest rate is %. (Type an integer or decimal rounded to three decimal places as needed.)
What annual interest rate is earned by a 17-week T-bill with a maturity value of $1,700 that sells for $1,680.88? ... The annual interest rate is %. (Type an integer or decimal rounded to three decimal places as needed.)
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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![**Title: Calculating Annual Interest Rate for a T-bill**
**Introduction:**
Understanding how to calculate the annual interest rate for a Treasury bill (T-bill) is essential for anyone involved in finance or investment. This practice helps in determining the profitability of such financial instruments.
**Problem Statement:**
*What annual interest rate is earned by a 17-week T-bill with a maturity value of $1,700 that sells for $1,680.88?*
**Calculation:**
To find the annual interest rate, follow these steps:
1. Determine the discount: Subtract the purchase price from the maturity value.
\[ \text{Discount} = \$1,700 - \$1,680.88 \]
2. Calculate the interest earned: Divide the discount by the purchase price.
3. Annualize the rate of return: Convert the 17-week rate of return to an annual rate.
**Formula:**
\[ \text{Annual Interest Rate} = \left( \frac{\text{Discount}}{\text{Purchase Price}} \right) \times \left( \frac{52 \text{ weeks}}{17 \text{ weeks}} \right) \times 100\]
**Solution:**
The annual interest rate is \[\boxed{\_}\]%
(Type an integer or decimal rounded to three decimal places as needed.)
**Conclusion:**
By applying these calculations, you can derive the annual interest rate from the given data, allowing you to make informed investment decisions.
**Note:**
For the accurate calculation, input the values into the formula and solve, ensuring all steps are followed methodically.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fc3ef53-ef76-4c8f-9c49-6c2ebf0a14b7%2Fc74d5c81-5dd7-4fed-8ce6-47b23c65e3da%2Fypp9dh9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Calculating Annual Interest Rate for a T-bill**
**Introduction:**
Understanding how to calculate the annual interest rate for a Treasury bill (T-bill) is essential for anyone involved in finance or investment. This practice helps in determining the profitability of such financial instruments.
**Problem Statement:**
*What annual interest rate is earned by a 17-week T-bill with a maturity value of $1,700 that sells for $1,680.88?*
**Calculation:**
To find the annual interest rate, follow these steps:
1. Determine the discount: Subtract the purchase price from the maturity value.
\[ \text{Discount} = \$1,700 - \$1,680.88 \]
2. Calculate the interest earned: Divide the discount by the purchase price.
3. Annualize the rate of return: Convert the 17-week rate of return to an annual rate.
**Formula:**
\[ \text{Annual Interest Rate} = \left( \frac{\text{Discount}}{\text{Purchase Price}} \right) \times \left( \frac{52 \text{ weeks}}{17 \text{ weeks}} \right) \times 100\]
**Solution:**
The annual interest rate is \[\boxed{\_}\]%
(Type an integer or decimal rounded to three decimal places as needed.)
**Conclusion:**
By applying these calculations, you can derive the annual interest rate from the given data, allowing you to make informed investment decisions.
**Note:**
For the accurate calculation, input the values into the formula and solve, ensuring all steps are followed methodically.
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