Discount rate. Future Bookstore sells books before they are published. Today, they are offering the book Adventures in Finance for \( \$ 12.85 \), but the book will not be published for another 2 years. The retail price when the book is published will be \( \$ 26 \). 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.)

To find the discount rate, we can use the formula for the present value (PV) of a future cash flow (CF): \[ PV = \frac{CF}{(1 + r)^n} \] In this scenario, the present value is the price the bookstore is offering today, \( \$ 12.85 \), and the future cash flow is the retail price, \( \$ 26 \), which will be received in 2 years. Rearranging to solve for the discount rate \( r \): \[ 12.85 = \frac{26}{(1 + r)^2} \] Multiplying both sides by \( (1 + r)^2 \) gives: \[ 12.85(1 + r)^2 = 26 \] Dividing both sides by \( 12.85 \) gives: \[ (1 + r)^2 = \frac{26}{12.85} \] Now calculating: \[ (1 + r)^2 \approx 2.0234 \] Taking the square root: \[ 1 + r \approx 1.421 \] Subtracting 1: \[ r \approx 0.421 \text{ or } 42.1\% \] Thus, the discount rate Future Bookstore is offering its customers for this book is approximately \( 42.10\% \). Now, it’s your turn to dive deeper! Did you know that the concept of discount rates dates back centuries, with early examples appearing in the works of mathematicians and economists from the Renaissance period? The idea of time value of money is rooted in the understanding that a dollar today is worth more than a dollar in the future due to potential earning capacity. If you’d like to explore the world of finance further, consider reading about the Time Value of Money, which covers concepts such as present and future value extensively. You can also check out online courses about financial modeling or investment analysis, where these principles are applied interactively through real-life scenarios!