How is the discount rate calculated according to the provided information?

The formula for calculating the discount rate, as indicated by the answer choice, is derived from the relationship between the present value (PV), future value (FV), and the time period (t). In finance, the discount rate is crucial as it helps in determining the present value of future cash flows.

The correct expression, r = [FV/PV]^(1/t) - 1, reflects the process of finding the annualized rate of return that equates the present value with the future value over time. Here’s how it works:

1. Future Value (FV) refers to the amount of money expected at a future date.

2. Present Value (PV) is the current worth of that future amount, discounted back at a certain rate over time (t).

3. The expression inside the brackets, [FV/PV], calculates the growth factor of the investment over the period.

4. Taking the t-th root (using the exponent 1/t) adjusts this growth factor to determine what the growth rate would need to be over each individual time period to achieve this future value.

5. Subtracting 1 from this result converts the growth factor back into a rate of return.

This formula captures the essence of compounding