Question
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Discount rate. Future Bookstore sells books before they are published. Today, they are offering the book Adventures in Finance for \( \$ 15.98 \), but the book will not be published for another 2 years. The retail price when the book is published will be \( \$ 21 \). What is the discount rate Future Bookstore is offering its customers for this book? What is the discount rate Future Bookstore is offering its customers for this book? (Round to two decimal places.)

Ask by Mullins Morgan. in the United States
Jan 22,2025

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Tutor-Verified Answer

Answer

The discount rate is approximately 23.90%.

Solution

To find the discount rate offered by Future Bookstore for the book "Adventures in Finance", we need to calculate the discount rate using the formula: \[ \text{Discount Rate} = \left(1 - \frac{\text{Discounted Price}}{\text{Retail Price}}\right) \times 100\% \] Given: - Discounted Price = $15.98 - Retail Price = $21 Substitute the values into the formula to find the discount rate. Calculate the value by following steps: - step0: Calculate: \(\left(1-\left(\frac{15.98}{21}\right)\right)\times 100\) - step1: Divide the terms: \(\left(1-\frac{799}{1050}\right)\times 100\) - step2: Subtract the numbers: \(\frac{251}{1050}\times 100\) - step3: Reduce the numbers: \(\frac{251}{21}\times 2\) - step4: Multiply: \(\frac{251\times 2}{21}\) - step5: Multiply: \(\frac{502}{21}\) The discount rate offered by Future Bookstore for the book "Adventures in Finance" is approximately 23.90%.

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To find the discount rate, you can use the formula for the present value (PV) of a future amount. The formula is given by: \[ PV = \frac{FV}{(1 + r)^n} \] Where: - \(PV\) is the present value (price today), - \(FV\) is the future value (price when published), - \(r\) is the discount rate, - \(n\) is the number of years until the book is published. Plugging in the values: \[ 15.98 = \frac{21}{(1 + r)^2} \] Rearranging gives us: \[ (1 + r)^2 = \frac{21}{15.98} \] \[ (1 + r)^2 = 1.313 \] Now taking the square root: \[ 1 + r = \sqrt{1.313} \approx 1.145 \] \[ r \approx 0.145 \text{ or } 14.5\% \] So, the discount rate Future Bookstore is offering its customers for this book is approximately **14.5%** when rounded to two decimal places.

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