Find the present value, using the present value formula and a calculator. (Round your answer to the nearest cent.) Achieve \( \$ 225,500 \) at \( 8.85 \% \) compounded continuously for 8 years, 135 days. Si................... Enter a number. fäl: Learn It: Calculate a Present Value Using the Compound Interest Formula.

To find the present value (PV) in this scenario, you can use the formula for continuous compounding: \( PV = FV \times e^{-rt} \), where \( FV \) is the future value, \( r \) is the annual interest rate, and \( t \) is the time in years. First, convert 135 days into years. There are 365 days in a year, so: \[ t = 8 + \frac{135}{365} \approx 8.36986 \text{ years} \] Now plug in the numbers: \[ PV = 225500 \times e^{-0.0885 \times 8.36986} \] You'll find that: \[ PV \approx 225500 \times e^{-0.7405301} \approx 225500 \times 0.477703 \approx 107,384.27 \] So, the present value is approximately **$107,384.27**. For a bit of historical background, the concept of present value dates back to the times of the ancient civilizations when merchants and traders would need to understand the worth of money over time, especially in the context of loans and investments. As commerce grew, interest calculations became essential for evaluating profitable opportunities, leading to the development of finance as we know it today. When it comes to real-world applications, understanding how to calculate present value is fundamental for personal finance decisions such as mortgage evaluations or investment appraisals. By grasping how much a future cash flow is worth today, individuals can make informed choices about where to allocate their money, ensuring they achieve their financial goals more effectively.