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 Today, they are offering the book Adventures in Finance for \( \$ 15.98 \), but the book will not be published for another 2 years.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? \( \square \) (Round to two decimal places.)

To find the discount rate, you can use the formula for the present value (PV): \[ PV = \frac{FV}{(1 + r)^n} \] Where: - \( PV \) is the present value (price today: \( 15.98 \)) - \( FV \) is the future value (price when published: \( 21 \)) - \( r \) is the discount rate - \( n \) is the number of years until publication (2 years) Rearranging the equation to solve for \( r \): \[ 15.98 = \frac{21}{(1 + r)^2} \] Solving this gives: 1. Multiply both sides by \( (1 + r)^2 \): \[ 15.98(1 + r)^2 = 21 \] 2. Divide both sides by \( 15.98 \): \[ (1 + r)^2 = \frac{21}{15.98} \approx 1.3133 \] 3. Take the square root: \[ 1 + r \approx \sqrt{1.3133} \approx 1.146 \] 4. Subtract 1 from both sides: \[ r \approx 0.146 \] 5. Convert to a percentage: \[ r \approx 14.6\% \] So, Future Bookstore is offering its customers a discount rate of approximately \( 14.60\% \) (rounded to two decimal places: **14.60**). --- To understand how discount rates work, it's essential to know that they serve as a bridge between the present and the future. The discount rate essentially tells you what the cash flows in the future are worth in today's dollars, making it a critical concept in finance, from corporate investments to real estate purchases. In practical terms, knowing the discount rate can help in making smarter purchasing decisions, as it allows customers to evaluate whether the cost of waiting for a product is justifiable compared to the present price. It can also aid businesses in setting pricing strategies to attract customers who might otherwise balk at paying full price for items yet to be released.